Insigne, 31, reached a deal with Toronto FC in January to join the club once the Serie A season was completed. He played 11 seasons with Napoli, which finished third in the league standings this past season.
The Reds were expected to debut Insigne on Saturday in a home game against the San Jose Earthquakes. After a minor injury in practice with his new club, he is now expected to miss the next three games and is targeting a debut with the club on July 23 at home against Charlotte FC.
"In the periods now where he's been on the field there's been discomfort and so he's been taken off the field," Toronto FC head coach Bob Bradley said after Wednesday's training.
"My guess is that it is going to take a few weeks to get him ready. I think a realistic target is going to be July 23. That's not official. There's always hope that things can move faster."
In 337 Serie A league games with Napoli, the Naples, Italy, native scored 96 goals. He has added 10 goals in 54 games with Italy's national team.
Insigne's four-year deal through 2026 with Toronto FC as a designated player officially began Friday. He reportedly will make $15 million per season.
The trade has been linked to another transaction, that of Toronto acquiring Italy international Federico Bernardeschi, who is available on a free transfer after his contract with Italian Serie A side Juventus expired.
Reuters contributed to this report.