The late-Saxon stone coffin is believed to contain someone important such as a king or bishop.
It was discovered earlier this year during an archaeological dig ahead of renovation work at the castle.
It was in the same area as the remains of a church, supporting the theory the skeleton is someone important.
A spokesperson for Lincolnshire County Council said: "The skeleton seems to wearing leather shoes or boots.
"Finding a sarcophagus from this period that's still in one piece is extremely rare, so the discovery is of national significance."
The sarcophagus was found three metres below ground level.
A facial reconstruction based on the skull will be created to show how the person would have looked, and the remains will be carbon dated to determine how old they are.
The church, which is at least 1,000 years old, was previously unknown.
An examination with an endoscope previously revealed the sarcophagus contained human remains.
Archaeologists began to remove the cracked lid in pieces, starting with the foot end, on Thursday.
The dig was undertaken as part of the Â£19.9m Lincoln Castle Revealed project, which will see the building of a new centre to house Lincoln's Magna Carta and a tower to provide access to the castle walls.
The project is due to be completed in 2015, when many of the finds from the dig will be put on display.
Archaeologists have opened a sarcophagus unearthed at Lincoln Castle and found a skeleton wearing what are thought to be leather boots or shoes.