Germans punished Chancellor Angela Merkel's centre-right coalition in a state election, depriving her of a majority in parliament's upper house after she angered many by agreeing to aid Greece.

The loss in the state of North Rhine-Westphalia is a blow to Ms Merkel little more than six months into her second term in office and means she will have to rely on opposition parties to deliver her policy agenda, which includes tax cuts.

An exit poll by ARD television put Ms Merkel's Christian Democrats on 34.5% and their Free Democrat allies on 6.5%, short of a majority and leaving the make-up of North Rhine-Westphalia's next government unclear.

The election was widely regarded as a referendum on Merkel's government and came just two days after her coalition voted in parliament to release billions of euros in aid to debt-stricken Greece - a move deeply unpopular with the public.

Separately, a chancellery official said Ms Merkel is not planning to reshuffle her cabinet after her finance minister was admitted to hospital suffering from an adverse reaction to new medicine.

Finance Minister Wolfgang Schaeuble's hospitalisation in Brussels intensified speculation about his capacity to stay in the job.

Mr Schaeuble, who has used a wheelchair since he was shot at a campaign rally in 1990, has been in and out of hospital several times this year.