Abdull, who played in England's last game against France at the end of 2021, suffered a quad tear and will visit a specialist to determine the severity of the injury.
Minchella, meanwhile, sustained ankle ligament damage and is expected to be out of action for up to six weeks.
Rovers took a gamble on Kane Linnett's torn bicep at Elland Road but he left the field early in the game and, as originally expected, is facing a lay-off of up to 12 weeks following surgery.
An injury update on Hull KR's website read: "The Robins’ medical staff have confirmed Elliot Minchella sustained an ankle ligament injury late in the game and will miss four to six weeks.
"Leaving the field in a similar fashion, Jordan Abdull suffered a quad tear in the loss and is set to see a specialist to determine the severity of the injury."
KR will also be without Sam Wood when they travel to the Mend-A-Hose Jungle to face Castleford Tigers on Sunday.
The versatile centre is likely to be sidelined for two to four weeks after suffering a dislocated patella in the recent loss at Leeds Rhinos.