No visitors have been allowed since March, when the Ukrainian authorities imposed a national lockdown to contain the spread of the novel coronavirus.
Pinchuk says the animals, born in captivity and used to the constant presence of people, are lonely. Some orang-utans even cry in their enclosures, he told Reuters.
"They don't understand what is going on, as the situation has changed. They were fine with the previous situation, they enjoyed people's company."
The zoo in the village of Demydiv, some 40 km (25 miles) from Kiev, has almost run out of money and can barely cover the utility bills needed to maintain the proper conditions for its animals, he said.
Zookeepers have had to adjust the animals' diet. Dozens of big cats are being fed with chicken, rather than more expensive pork or beef, and apples have replaced mangoes and pineapples for the monkeys.
Pinchuk urged people to donate to support the zoo, which is home to 400 animals including a seal, a hippopotamus and giraffes. Out of 70 staff members, the zoo has kept only 20, on a minimum salary.
"But it is not like this. There are animals who eat more than 100 kilos of food daily. We spend 500,000 hryvnia ($18,650) just on food per month."
The government is set to lift some lockdown restrictions on Monday but Pinchuk is not sure whether the zoo, which is approaching its fifth anniversary, will be allowed to re-open.