Senol Buran, cafeteria head at Cumhuriyet, was remanded accused of insulting the president. He denies the refusal was an insult, his lawyer said.
Turkey has cracked down on dissent since a failed coup in July.
Cumhuriyet staff have been among tens of thousands of people detained, suspended or sacked.
The newspaper is one of few to have taken an anti-Erdogan line.
Mr Buran was on his way to work on 24 December when he found roads were closed as part of security measures for a speech being given by Mr Erdogan.
Mr Buran told police officers: "I would not serve that man a cup of tea."
A judge at the Istanbul criminal court jailed Mr Buran pending a trial.
Insulting the president can carry a four-year jail term.
Last month, 10 Cumhuriyet staff members were jailed pending trial, suspected of giving support to Kurdish militants and the US-based cleric Fethullah Gulen, who Turkey blames for masterminding the failed coup attempt.
Its former editor-in-chief, Can Dundar, fled to Germany this year pending appeal against a jail sentence.
Mr Erdogan's critics have accused him of severely curtailing freedom of speech since the coup attempt, with more than 100,000 people sacked or suspended.
His supporters regard him as a strong leader who has been the driving force behind an economic boom.
The boss of a cafeteria at a Turkish opposition newspaper has been detained after saying he would refuse to serve tea to President Recep Tayyip Erdogan.