The Clooneys were accompanied to the meeting by David Miliband, the former UK foreign secretary and head of the International Rescue Committee.
Mr Miliband said they discussed solutions to the "global problem".
He praised Mrs Merkel for "showing very strong leadership" during the crisis.
The Clooneys planned to visit a Berlin refugee shelter later Friday. They are in Germany to attend the Berlinale film festival, where the actor is promoting his new film Hail, Caesar.
He had told reporters on Thursday that he would meet Mrs Merkel and, separately, a group of asylum seekers, "to talk about and ask what messages and what things we can do... to help."
Germany took in around 1.1 million asylum seekers in 2015 alone, but opposition is growing within the country against Mrs Merkel's so-called "open-door" policy.