Hargreaves made his return for United on Saturday against Wolves, but suffered a hamstring problem just four minutes into the game.
“We feel so sorry for him,” O’Shea told MUTV. “He was so looking forward to it and we were really excited for him as well after all the hard work he’s put in.
“We just have to wait and see exactly what the injury is, but he’ll be back again, no doubt about that. He’s worked very hard to get to this point and I’m sure there’ll be a few little niggles – he’s just got to get over them quickly.”