The Liverpool forward is currently at the World Cup in Russia with Egypt, whose training base is in the Chechen capital Grozny.
After a short speech during a ceremonial banquet at Kadyrov's residence on Friday, the Chechen leader pinned a brooch of the region's flag onto the striker's training shirt.
Salah was then presented with a silver plate and a signed shirt of Chechen football team FC Akhmat Grozny, the club which is named in honour of Kadyrov's late father.
"Mohamed Salah is an honorary citizen of the Chechen Republic. Yes, that's right! Tonight I signed a decree conferring this high award on the great footballer and member of the Egypt and Liverpool teams," Kadyrov wrote on social media.
Salah missed Egypt's World Cup opener against Uruguay before scoring a penalty against World Cup hosts Russia, but the North Africans' two defeats, combined with Uruguay's win over Saudi Arabia, have led to the Pharaohs' elimination from the tournament.