The German chancellor said the secrecy around the algorithms used by online platforms threatened open debate.
Without greater scrutiny, many people could get a distorted or censored view of events, she said.
Google and Facebook told German paper Der Spiegel they gave the public a lot of information about how they worked.
Mrs Merkel's call for action follows work by German politicians to investigate how the software works.
"This is a development that we need to pay careful attention to," Ms Merkel said in a keynote speech to the Medientage conference in Munich earlier this week.
"The big internet platforms, via their algorithms, have become an eye of a needle, which diverse media must pass through to reach users," she added.
"These algorithms, when they are not transparent, can lead to a distortion of our perception, they narrow our breadth of information," she warned.
Mrs Merkel called on the algorithms to be made public so "informed citizens" can see the influences on what they are fed via social media, news feeds and search results.
In many cases, said the German chancellor, information was drawn from a limited list of sources.
Scientist Cathy O'Neil, who has written extensively about the inner workings of data algorithms and their potential for harm, said most of the information Facebook shared was technical and rarely touched on how influential it was.
"What we have right now is an incredibly influential platform that has no reason to measure its influence because it will likely open it up to regulation," she said.
In late 2016, a cross-party group of German politicians will send the results of an investigation into algorithms used by Facebook, Google and other internet firms to the EU's digital commissioner Gunther Oettinger.
"The chancellor has touched on an important issue," Mr Oettinger told Der Spiegel [link in German].