Mr Merz, leader of the country’s CDU/CSU conservatives, is hoping to become the 10th chancellor since the end of the Second World War.
No candidate has failed to win on the first ballot since then.
Needing a majority of 316 out of 630 votes in a secret ballot, he received 310 – falling short by just six votes.
He had been expected to win the ballot comfortably after securing a coalition deal with the centre-left Social Democrats (SPD).
Parties will now regroup to discuss the next step. It is unclear how long that will take, but another vote could be held later on Tuesday.
The lower house of parliament – the Bundestag – has 14 days to elect a candidate with an absolute majority.
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