Following a meeting two weeks ago, the 55 member associations that make up UEFA, hoped to complete all games by June 30, when player contracts expire.
However, today, the decision was made to suspend them indefinitely.
The Euro 2020 qualifying playoffs and international friendlies planned for June have also been postponed.
The Champions League and Europa League are suspended at the round-of 16 stage with Atletico Madrid, Paris Saint-Germain, RB Leipzig and Atalanta the four sides to have qualified for the quarter-finals.
Manchester City vs. Real Madrid, Juventus vs. Lyon, Barcelona vs. Napoli and Bayern Munich vs. Chelsea are the four round-of-16 second-leg ties have yet to be played.