Bosses at Paignton Zoo and Living Coasts say they will not be in a position to reopen on Monday - despite the Government expected to give the official go ahead later on.
A spokesperson for Wild Planet Trust said: "When we were forced to close on Monday 23rd March, we furloughed all non-essential staff in order to save costs so that we could be in a position to re-open when we were allowed later in the year.
"While the zoos have been closed we have had no income, apart from a small amount of funds kindly raised by our supporters through our fundraising campaign.
"This means that we have not had the staff working in order to the get the zoos ready to open earlier than we expected. We are already £3 million down on our expected financial position at this time of year.
"It was announced on 11th May that outdoor ticketed venues would not be able to open until 4th July at the earliest. After recent lobbying from some of the larger UK zoos to be able to open earlier, on Monday 1st June Government responded by legally closing zoos, aquariums and safari parks indefinitely! So we were still working to a re-opening date in early July.
"Whilst we have been planning for weeks for our re-opening, we have delayed implementing those plans because of the cost of bringing staff back from furlough. We were anticipating an announcement on or about 18th June allowing us to re-open in early July, that would give us the confidence to unfurlough essential staff. We will now do so but it will still take us some time to be ready.
"When we are in a position to re-open, all of our indoor exhibits will be required to remain shut, so we will have to offer a discounted ticket price and restrict the number of guests coming through our doors. With the extra costs involved in implementing the required social distancing measures we have ongoing concerns about the longer term future of our zoos with fewer visitors, higher operating costs and the possibility of further ‘lockdowns’ in the future."