MEXICO CITY, Dec. 26— Some of Mexico's most treasured pre-Columbian artifacts were stolen from the National Museum of Anthropology on Christmas Eve, authorities said today.

In all, 140 objects made of gold, jade, obsidian and turquoise, crafted by the Mayas, Aztecs, Mixtecs and Zapotecs before the Spanish conquest of Mexico, were discovered missing Christmas morning. They had been in seven glass cases in three of the museum's galleries on the first floor and in a basement exhibition area.

Symbol of Cultural Heritage

The museum, in Chapultepec Park in the heart of Mexico City, is one of the city's most famous tourist attractions. The museum and its contents are regarded by Mexicans, who are fiercely proud of their Indian heritage, as one of their national treasures, a symbol of the cultural richness of the advanced civilizations that existed in Central America before the arrival of the Europeans in the 16th century.

Among the objects taken were a famed Aztec carved obsidian jar representing a monkey, most of the relics from a sacred well near the Mayan city of Chichen-Itza and most of those from the Palenque tomb, in which a Mayan ruler was buried with many objects of jade. Also missing were artifacts from Tomb No. 7 in Oaxaca, including the Zapotec mask of the bat god. Gold necklaces, pendants and ear ornaments were among the objects removed.

Museum officials, in a statement, said the thieves, who apparently had extensive knowledge of pre-Columbian art, took objects that were small and easy to carry but that probably would have the highest value in the thriving international market in stolen pre-Columbian artifacts.

In a news conference late in the day, museum officials said the museum had no electronic alarm system. Instead, it relies on eight guards and a captain who patrol the three floors of the building. The officials said that every two hours a guard was supposed to pass through every area of the museum.

They declined to speculate about how the thieves might have avoided the guards. The removal of the artifacts from their cases was easy, since the cases were not locked and did not have alarms.

When questioned about insurance, museum officials would say only that when artifacts are sent out of the museum, they are insured.

The thefts were discovered on Christmas Day at 8 A.M., during the changeover of the guards.

The Federal Attorney General's office and its police force, the Mexican Federal Judicial Police, began an investigation. A spokesman for the Attorney General said the eight guards on duty were being questioned but were not under arrest.

''We have no idea how the theft took place and it would be precipitous at this point to give an opinion on how it might have taken place until the guards have been fully interrogated,'' said Felipe Flores, the spokesman for the Attorney General's office.

Mexican authorities said that they had alerted museums around the world and that customs agents were ''reinforcing their vigilance.''

The museum, designed by the architect Pedro Ramirez Vazquez and opened in 1964, consists of two floors and a basement. Galleries on the ground floor open onto a courtyard.

The thefts occurred in the Mixtec, Maya and Oaxaca rooms, which open onto the courtyard, and in the basement area where a replica of the Palenque tomb stands and within which the genuine artifacts were displayed.

'They Stole Only Masterpieces'

''The people knew exactly what they wanted because they stole only masterpieces,'' said Teodoro Maus, the Cultural Attache at the Mexican Consulate in New York City.

''The objects have been taken by criminal hands that surely are tied to the world traffic of cultural treasures that is a constant danger to all museums of the world,'' the museum officials said.

Dealers in Mexico's underground market in pre-Columbian artifacts traffic mostly in objects stolen from archeological sites, illegally exporting them to collectors.

''There's a very strong underground traffic of people who buy pieces, and it's stronger with private collectors than with museums or auction houses,'' Mr. Maus said. ''No institution will buy them because they are registered and obviously stolen. But a collector can buy them and put them in his basement.''

The obsidian monkey jar is considered one of the most valuable objects taken. It was crafted by the Aztecs and represented the god of dance, play and love.

'A Difficult Material'

''It is a tour de force in dealing with material, as obsidian is a difficult material to work with,'' said Julie Jones, curator of primitive arts at the Metropolitan Museum of Art in New York.

The gold objects from the museum's Oaxaca Room, which contains artifacts from the Zapotec and later Mixtec cultures, is also considered a serious loss. The gold ornaments from Tomb No. 7 in Oaxaca are of particular archeological value because they are among the only such pre-Columbian ornaments to come from a dated tomb. Most similar objects were plundered by Spanish conquistadors or were taken by grave robbers over the centuries.

Also taken from the Oaxaca collection was the Zapotec mask of the ''murcielago,'' or bat god, an equisite work of green stones and seashell mosaic.

The Palenque tomb, which was discovered near Villahermosa in southern Mexico, dates from A.D. 600 to 900. The other major Mayan objects taken came from a well in Chichen-Itza, where offerings to the gods were made with jade, jewels, disks carved in gold and other objects. Most of the objects recovered from the well were taken.

The courtyard of the museum is a favorite place for conferences and meetings that play upon Mexican nationalist feelings. When Mexico's President, Miguel de la Madrid, set up a national earthquake reconstruction commission after the September catastrophe, he chose the museum courtyard as the setting for the installation ceremony.

When one scholar, in a speech at the ceremony, equated the grandeur of the setting with the glory of the Aztecs and Mexico's ancient races, he received thunderous applause.

photo of police in Mexico (Reuters) (page C28); photos of some stolen artifacts