The leaders were seated in the Oval Office posing for cameras when the press asked if the two would give them a handshake.
Merkel turned to look at Trump, who didn't respond or make eye contact with the chancellor. She then flashed a smile to the cameras.
The press conference was already less than warm, as Trump warned Merkel earlier that trade relations between Germany and the U.S. may be under review soon.
"The U.S. has been treated unfairly, and that's going to stop," Trump said.
The two leaders did ultimately shake hands later during the press conference.
Correction: This story has been updated to reflect when President Donald Trump appeared to ignore requests for a handshake with German Chancellor Angela Merkel.