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Kylian Mbappe wore the captain's armband in Tuesday's (AEDT) 7-0 Coupe de France win over sixth-tier Pays de Cassel in the absence of regular skipper Marquinhos.
Speaking after the cup rout, Galtier said Mbappe, who scored five times, "deserves" to be second captain when Marquinhos is not available.
Kimpembe, who has not played since November because of a heel injury, took to social media to state he had not been previously informed about Galtier's decision.
However, PSG head coach Galtier has since discussed the matter with Kimpembe to clear up any misunderstanding.
"I expressed myself badly on Monday [Tuesday AEDT]," Galtier said at a pre-match press conference ahead of Monday's (AEDT) Ligue 1 match with Reims.
"The choices are very clear: Kylian is one of the vice-captains. Every time Kimpembe has been on the field and Marquinhos hasn't been, Kimpembe has had the armband.
"When Marquinhos isn't available, there is another captain. In the Lens match there was neither Kimpembe, Marco [Verratti] nor Marquinhos, so Kylian was captain.
"I decided to have Kylian as captain in the last game because he is one of the vice-captains, not 'the' vice-captain. I've had a discussion with Kimpembe to explain all this."
PSG's victory against Pays de Cassel came on the back of a 1-0 loss to Rennes in its most recent Ligue 1 match as its lead on Lens at the summit was cut to three points.
However, not since September 2020 has it lost successive league matches, while its return of 47 points after 19 matches is its fifth-best ever at this stage.
The reigning champion faces a tough test this weekend, though, as it hosts a Reims side unbeaten in 11 Ligue 1 games – the longest run of any side in the division.
"It will be a difficult match for us to begin this run of games," Galtier said. "They have changed system and coach, and we know it will be a challenge for us.
"We now have Kimpembe back in training and Marco Verratti is back with the group. We have to cope with the calendar and focus more on recovery."
PSG is unbeaten in its past 31 Ligue 1 games at Parc des Princes, winning 27 of those, and has scored in each of the past 20 on home soil.
