A chimpanzee couple named Adam and Eve smashed windows to get out of their enclosure at the Sa Coma Safari Zoo on Monday.
Eve was surrounded as she neared the town of Son Carrio and shot dead.
Local media say that Adam is believed to be hiding in a wooded area close to residential housing.
Police have closed off a nearby road to try to prevent the 80kg (176lb) chimpanzee from reaching a nearby tourist area and beach front, according to reports.
How the animals managed to escape is not yet known.
"It is not very clear, but it seems they broke the bars of their cage," a spokesman for Spain's Guardia Civil told AFP news agency.
"These animals are very strong. They can lift double their weight."
Animal rights groups have criticised the shooting of Eve.
Police said the chimpanzee had been killed because she had become "very agitated" and there was a risk she might attack a member of the search party.
Police in Spain are searching for a chimpanzee in Majorca, two days after it escaped from a zoo popular with tourists.