In an Instagram post, the 17-year-old stressed she had "basically recovered" after developing symptoms following a trip around central Europe.
The Nobel Peace Prize nominee stressed the "enormous responsibility" young people and those not in high risk groups have.
She wrote: "Our actions can be the difference between life and death for many others."
The climate campaigner addressed crowds of 30,000 in Bristol at the end of February, before going on to attend an Environment Council meeting in Brussels in early March.
After returning from the trip, the Swedish teenager said she self-isolated as a precaution.
Ten days ago, Greta said she had developed symptoms including "shivers, a sore throat, and a cough".
Though she had not been tested for Covid-19, Greta wrote it was "extremely likely" she had contracted the virus based on "combined symptoms and circumstances".
The 17-year-old stressed the virus had not made her feel too ill, writing: "THIS IS THE BOTTOM LINE: I almost didn't feel ill."
Addressing her huge youth following, the climate activist said "many (especially young people) might not notice any symptoms at all".
As stay-at-home restrictions increasingly strengthen across Europe, Greta urged her followers to "follow the advice from experts and your local authorities".
The teenager stressed: "#StayAtHome to slow the spread of the virus."
Last week, the Government’s top scientific advisors warned young people not to be complacent over Covid-19 as they urged the public to keep up social distancing measures to protect themselves.
England’s Chief Medical Officer Professor Chris Whitty said the vast majority of people in all age groups would recover but it was a mistake for young people who are healthy to think they would all just "breeze through" the pandemic.
Prof Whitty said: "It is clear that children get this disease much less strongly than adults, I think the data on that is pretty strong now, and it certainly is the case that the majority of those that end up dying sadly are people who tend to be either in the later part of their lives, usually quite elderly, or those with pre-existing health conditions."
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He added: "But there are also some young people who have ended up in intensive care or who have ended up with severe disease around the world.
"I think it’s important that we don’t give the impression that every single person who is young and healthy is just going to breeze through this."
He said the "great majority" of people will suffer no symptoms or mild to moderate symptoms, but a very small proportion of young people "will have severe disease even though they are young and healthy".