He acknowledged on Sunday the scale of the "sacrifice" the public is taking but said he could not make "an accurate prediction" on how long it must be endured.
The Chancellor of the Duchy of Lancaster's warning came after the UK's death toll passed 1,000 and Boris Johnson wrote to every household with a warning he could impose stricter measures.
But Mr Gove declined to say what the tougher rules could look like with the public confined to their homes for all but essential travel and for once-daily exercise.
"Everyone is making a sacrifice and I appreciate the scale of that sacrifice," he told the Andrew Marr Show.
Join our new coronavirus Facebook group for the latest confirmed news and advice as soon as we get it www.facebook.com/groups/yorkshirecoronavirus"But the reason all of us are making these sacrifices is because all of us will have people whom we love who are at risk from this virus.
"I can't make an accurate prediction, but everyone does have to prepare for a significant period when these measures are still in place."
Mr Gove declined to be drawn on one key scientist's estimate of June being the earliest like month that they could be eased, but warned the lockdown will last longer if the rules are not obeyed.
"It depends on all of our behaviour. If we follow the guidelines, we can deal more effectively with the spread of the disease," he told Sky's Sophy Ridge on Sunday.
But the positive message he delivered was that the public appear to be heeding the advice.
"At the moment, all the evidence is that people are observing the rules, if you look at the number of people on public transport that has fallen, if you look at footfall in supermarkets and other stores, that has fallen as well," he said.