The 28-year-old striker has been struggling with the same knee problem that hampered him last season. He joins defender Carles Puyol on Frank Rijkaard's injured list.
Gudjohnsen has been linked with a summer move elsewhere following the arrival of Thierry Henry at the Nou Camp, but in the absence of any offers for the former Bolton and Chelsea man, it now seems likely he will stay with the club he joined a year ago.
Also missing from the games against Dundee United and Hearts will be Lionel Messi, Gabriel Milito and Rafael Marquez, who have all just recently returned from international duty at the Copa America.
Drenthe keen to make Madrid move
However, new recruit Henry will make his debut for the Catalans in Scotland. The former Arsenal striker joins Ronaldinho, Lilian Thuram, Samuel Eto'o, Gianluca Zambrotta and Xavi in the squad for the games at Tannadice on Thursday and Murrayfield on Saturday.