Markus Söder said it was a terrible day and called for a pause: “We mourn the loss of a small, innocent child.”
Police said they were investigating a motive and the background to the attack remained unclear. The suspect was said to have been staying in accommodation for asylum seekers.
Chancellor Olaf Scholz, who was on a visit to France, condemned an “unbelievable act of terror”. He posted on social media that he was tired of seeing “such acts of violence every few weeks” and urged authorities to find out why the suspect was still in Germany.
The German government has come under increasing pressure to take a harder line on immigration after a number of fatal attacks, and with federal elections due on 23 February, the anti-immigration, far-right AfD is second in the polls.
Five people were killed when a man rammed his car into a crowd at Magdeburg’s Christmas market in December. A Saudi doctor has been charged with the attack.
In August, three people were fatally stabbed in the town of Solingen. The suspect was a Syrian national facing deportation after a failed asylum.
That attack led to the German government expanding border checks and tightening controls on knives, and fuelled an intense debate over asylum rules that has continued in the run up to next month’s election.
The conservative Christian Democratic Union (CDU) currently lead the polls and Olaf Scholz’s centre-left Social Democratic Party (SDP) are behind in third place.
The election was called after Scholz’s three-party coalition collapsed in November.