Salah played in Egypt's second World Cup game of the tournament, which saw them knocked out after a 3-1 defeat to hosts Russian Federation.
'Mohamed Salah is an honorary citizen of the Chechen Republic.
The Egyptian Football Association says there is "no problem" between it and star player Mohamed Salah, amid reports the Liverpool forward could be set to quit the national team.
He returned for Egypt's 3-1 loss against the hosts but was not at his sharpest despite scoring a penalty.
Colombia’s triple hammer blow dumps Poland out of World Cup
Yerry Mina nodded in James Rodriguez's cross shortly before half-time to put the South Americans ahead. Poland played well for 15 minutes but then faded.
In the social media post, Mr Kadyrov added that he wants Egypt to return to Chechnya after the World Cup for a friendly against local club Akhmat Grozny - named after his father, who was assassinated in 2004.
But Salah is now believed to be weighing up his global future. "I gave Mohamed Salah a copy of the order and a pin at a celebratory dinner that I gave in honour of the Egyptian team". The Chechen leader posed for pictures with Salah while pinning a medal on his chest.
The Liverpool talisman was also captured smiling during a speech from Kadyrov, with Salah reportedly unhappy at being used as a political image and eager to only get involved in topics about football.
Salah was honoured during a banquet held to bid farewell to the Egypt squad held at Kadyrov's presidential palace in Grozny on Friday night.
Vodafone has a sponsorship deal with Salah, but his image was plastered on Egypt's World Cup plane which was sponsored by WE, a rival telecommunications company. Given the vocal Tweets from his agent, Ramy Abbas Issa, it's at the very least clear that all is not well in the Salah camp. In an interview with BBC, he said: "Everyone has played here, even Maradona at our stadium, but we don't use this kind of thing for politics".