BERLIN—Nearly 24 hours after Germany’s deadliest terror attack in decades, police said they had been holding the wrong man as their only suspect, reviving fears of more violence and escalating the hunt for at least one perpetrator at large.

Amid the uncertainty over who plowed a truck through a crowded Christmas market, the attack that left 12 people dead and 14 people still in critical condition posed new challenges for Chancellor Angela Merkel. She and her government moved to confront the attack’s political impact given...