The band - made up of Matt Healy, 31, George Daniel, 30, Adam Hann, 32, and Ross Macdonald, 31 - were due to begin an European tour next month.
They also revealed they are currently in the process of making a new album, but while Matt admitted that it won't be released for a while, 'other stuff' will be out in the meantime - likely music from the band's side-project, Drive Like I Do.
The 1975 shared the notice on their Instagram on Tuesday, saying: 'We are really sorry to announce that we have made the decision to cancel all scheduled touring for 2021.
'These are incredibly difficult times for a lot of people, and until we can be sure that we will be able to play shows in a way that is safe for our fans and crew, we have decided the best course of action is to cancel our touring so that, where possible, everyone can get their tickets refunded sooner rather than later.
'We're currently making a new album and look forward to seeing you all at a show as soon as it is safe to do so.
'For information on refunds for Finsbury Park please go to your point of purchase. Stay safe and look after each other. Matty, George, Adam and Ross x' [sic]
The tour was due to start on February 12 in Copenhagen, Denmark, and end in Barcelona, Spain, on March 9.
They were also due to give a performance at Finsbury Park in London in July and at various festivals across Europe this summer, including Boardmasters in Newquay.
Matt also shared the notice on his own Instagram account, captioning it: 'This is so s*** as I love attention, especially on a stage with loads people shouting "I love you!" or "rat lives matter! or "play antichrist!
'Unfortunately The 1975 live is not something for 2021.
'I already love the new album we are making and I hope you will too. That won't be out for ages. Other stuff will be tho'
Lockdowns and social distancing measures across Europe mean large groups of people cannot gather indoors.
© Associated Newspapers Ltd.