The centre-back took to social media to vent his frustration at the lack of communication within the club after manager Christophe Galtier announced the decision.
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Kimpembe has been one of PSG's deputies for regular captain Marquinhos, with Marco Verratti another star to have worn the armband in the absence of the Brazilian.
However, with the skipper rested, Mbappe was the man given the armband for PSG's French Cup clash against sixth-tier minnows Pays de Cassel - a game in which he scored five goals in a huge 7-0 victory for the Ligue 1 giants.
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After the win, Galtier was asked about Mbappe being named captain and remarked that he has been the club's vice-captain since the summer.
And it appears Kimpembe - who is currently sidelined with an Achilles tendon injury - wasn't told about the change, as he wrote on Instagram: "In the last few hours I have been able to hear and read a lot about myself.
"I therefore wish to make things clear in order to avoid continuing to spread false information in this regard.
"I was not made aware of this decision, this is completely false…
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"That said, I will always respect the decisions of the club."
Kimpenbe came through the youth ranks at PSG and has made 232 senior appearances for the club.
He last wore the captain's armband on October 29 in a game against Troyes, despite the fact Mbappe - who was apparently named vice-captain in the summer - also started.
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That has caused confusion, not least with one of their own players with the 27-year-old centre-back appearing to have had his leadership position in the team stripped without his knowledge.
Galtier could clarify the situation ahead of PSG's next Ligue 1 clash at home against Reims on Sunday.