Hamren gave Celta Vigo striker John Guidetti a chance to stake a claim for a starting spot alongside Ibrahimovic and the 24-year-old put in an energetic performance, almost breaking the deadlock with a curling second-half shot that flew just over.
Sebastian Larsson also took a free kick from a dangerous position for the Swedes, but he too could not keep the ball down and it flew harmlessly over the bar.
With midfielder Kim Kallstrom resting a tight groin and Albin Ekdal still recovering from a back injury, Sweden lacked a player with the passing ability to unlock Slovenia's defence.
The visitors threatened several times on the break but goalkeeper Andreas Isaksson, having been made captain in Ibrahimovic's absence, was in no mood to spoil the occasion by conceding a goal.
With lots of empty seats at the Swedbank Stadium, the biggest cheers on the night were reserved for hometown favourite Ibrahimovic, whose every appearance on the big screens was met with rapturous applause.
Sweden take on fellow Euro 2016 finalists Wales in their final pre-tournament friendly in Stockholm on Sunday before heading to France, where they will face Italy and Belgium as well as Ireland in Group E.
(Reporting by Philip O'Connor; editing by Ken Ferris)
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