In the middle of The Paramedic (2020), the radio news announced:
"Friday, January 3, 2020... According to information from Chinese media, the cause could be a virus that originated in a live animal market in Wuhan."
So it is strongly suggested that the movie is set at the beginning of the COVID-19 outbreak.
What is the first movie that is set in a world having the COVID-19 pandemic?
- Only feature-length movies are considered.
- The movie has to be fiction, not a documentary about COVID-19.
- The world in which the movie is sets has COVID-19. This could be deduced, for example, by TV news in the movie.
- The events of the movie do not necessarily happen during COVID-19. They can happen before or after.
Honorable mentions (not fitting all criteria)
The Paramedic. As mentioned in the question, the movie only strongly suggest that it is the beginning of COVID-19 pandemic, but COVID-19 is not mentioned explicitly.
Love in the Time of Corona an American romantic comedy television miniseries created by Joanna Johnson that premiered on Freeform on August 22, 2020. (suggested by Darth Locke)
Social Distance upcoming (October 15, 2020) series for Netflix. (suggested by Darth Locke)
N95 by Ivan Theophilus, short film has been published on 8th March. (suggested by Matt)