According to Russian news outlet Tass, Pogrebnyak posted pictures from his trip to Italy on social media, tipping off Dynamo about where he'd been, and now faces being fined or even sacked by the club as a result.
The 34-year-old has barely played this season, featuring only once in the league. He has largely been on the bench as an unused substitute, but had been left out of the matchday squad altogether for four straight games before the Anzhi clash.
He was once more left out against Anzhi, but opted to travel to Italy instead of fulfilling his contractual obligation to Dynamo and remaining with the rest of his team-mates even though he wasn't going to be involved.
A source told Tass that, in doing so, Pogrebnyak 'violated the terms of his contract'.
As such, Dynamo are believed to have opened an investigation against Pogrebnyak.
The striker, who was part of the Russia squad at Euro 2012, enjoyed the best seasons of his career at Zenit St Petersburg between 2007 and 2009, winning the Russian Premier League, the UEFA Cup, the Russian Super Cup and the UEFA Cup in three seasons with the club.