The Diergaarde Blijdorp zoo was evacuated and the 11-year-old gorilla, named Bokito, was eventually contained in a restaurant within the park, police spokeswoman Yvette de Rave said.
Four people were injured, including the woman who was bitten, zoo director Ton Dorrestijn said.
Bokito was shot with a sedative dart and recaptured, said zoo spokeswoman Lilian Jonkers, but she couldn't say what his condition was. It was not immediately clear how he managed to climb the high stone walls surrounding his enclosure.
"He got over the moat, which in itself is remarkable, because gorillas can't swim," Dorrestijn said. "He got onto a path for visitors and started running and went at full speed through tables and diners at the Oranje restaurant."
A witness, Robert de Jonge, told NOS radio that he didn't see the gorilla escape but began following it and tried to help after he saw people running and screaming that the animal had grabbed a woman.
"I saw the beast running through the park with a woman behind him, him grabbing her forearm," De Jonge said.
At a distance of around 30 yards, he saw the gorilla lie down near the woman and then heard her scream.
"He bit her, or I think he bit her, because when he stood up his mouth was covered in blood," De Jonge said.
He said he then stopped to tell arriving police what had happened and ran with them as they traced the gorilla to a nearby restaurant terrace.
The zoo was packed with visitors as many Dutch took advantage of a national holiday Thursday to make a long weekend. "Everyone was in panic, running away, screaming, wailing, screaming kids running around, I don't know what all, kids without parents — it was a total drama," De Jonge said.
Children cowered in their parents' arms as the gorilla loped past. People tried to hide inside the restaurant and were trying to bar the door, but fled as the gorilla approached, De Jonge said. Bokito then punched through the glass door and ran inside.
"They were all in panic — the animal, too, I mean — and all the people ran outside the restaurant, and zoo personnel were running up and they were able to keep the animal inside by barricading the doors with garden furniture and things," he said.
De Jonge said he later saw the woman "covered in blood," but walking unaided.