Kean, 21, will not travel for PSG's Ligue 1 match with Bordeaux on Wednesday after contracting the virus.
"He's staying in Paris... he'll respect isolation and is subject to the appropriate health protocol," the club said.
PSG face Barca at the Parc des Princes in the last 16, second leg Champions League clash next Wednesday, heavy favourites to make the quarter-finals after cruising to a 4-1 win in the first leg at the Camp Nou.
Kean has been in good form in recent weeks, scoring four times in his last five appearances in all competitions including one in that thumping of Barca last month.
He has scored 11 goals in Ligue 1 since arriving on loan from Everton in October.
Kean's last-minute absence leaves coach Mauricio Pochettino without four of his attacking stars for the match at Bordeaux, with Neymar, Kylian Mbappe and Angel Di Maria all out of the trip south.
PSG are two points behind league leaders Lille, who face Marseille on Wednesday, with Lyon and Monaco a further one and two points back respectively in a tight title race.
