The 24-year-old is in the national team squad for the upcoming World Cup qualifiers with Peru and Argentina next month.
Morelos, along with a team physio who also tested positive, will isolate as per guidelines.
The striker, who helped Rangers win the Scottish Premiership, is hoping to be part of the squad for this summer’s Copa America.
A statement from the Colombian FA confirmed the player is in “good health”.
:"The technical staff of the Colombia male senior team reports that, following biosafety protocols, RT PCR tests were carried out and two positive cases for Covid-19 were found, the player Alfredo Morelos and the kinesiologist José Rendón,” it read.
"After knowing the positive results, following the protocols, the respective isolation of the two people was carried out, who at the moment are in good health."