Mina has been a regular at centre-back this season, appearing in 25 of Everton's 29 top-flight games and scoring twice.
However, there appears little prospect of him being available when the league resumes later this month.
His club stated on their website: "Everton Football Club can confirm Yerry Mina is set to be sidelined for several weeks after sustaining a muscle injury.
"A scan confirmed the Colombia international suffered a partial tear in his left quad muscle during training last week.
"The 25-year-old is now in the early stages of his rehabilitation under the care of the club's medical staff and making good progress."
Mina was an eye-catching €30million signing from Barcelona in August 2018, just weeks after scoring three goals for his country in the World Cup.
The 2019-2020 Premier League season is due to return from a three-month coronavirus suspension when two games are played on 18 June (AEST), followed by a full programme of weekend fixtures.
Everton sat 12th in the Premier League when the season was halted, six points behind sixth-placed Wolves.
News of Mina's injury comes after last week's setback to Everton, that saw midfielder Jean-Philippe Gbamin suffer a severe Achilles injury in training that will keep him out for the rest of the season.