Officials from Soho Square will ask the Uruguayan to explain his allegation that the referee has an agenda against the duo which dates back to when they were both players.
The former Chelsea and Spurs midfielder could now face a fine and a touchline ban.
Poyet had said after Tuesday's defeat: "I don't want to see Andy D'Urso at a Leeds match again.
"He cannot forget what he did to Dennis and me as players and it has continued into management."
Poyet recalled both he and Wise had been sent off by D'Urso during their playing days and claimed it was "personal and very sad".
He added: "He is always laughing on the pitch, but won't give any hard decisions. When there is something complicated in the box, he won't give anything at all."
The likeliest outcome is that the FA will write to Poyet asking him to explain what he said at a post-match media-briefing, in which he took Wise's place.
Poyet admitted Portsmouth "were great and deserved their win" but he insisted his side should have been awarded a penalty.