John Foley -- Peloton's founder and CEO -- sent a letter to his more than 600k subscribers Monday, letting them know the company is yanking any classes that use the songs ID'd in that lawsuit a handful of music publishing companies filed.

TMZ broke the story ... the publishers claim Peloton was using a bunch of hit songs from big-time artists without permission -- upwards of at least a thousand tracks, apparently -- ranging from Rihanna's "Umbrella" to Pat Benatar's "Hit Me With Your Best Shot."

Those companies are suing for major damages ... up to $150 million.

In his letter, Foley says the fitness company is only doing this as a precaution ... and assures users that their cycling experience will not be affected by the change. He says Peloton has deals in place with lots of other music publishers and labels that give them access to a "broad catalog" of music that he suggests will be able to replace the temporarily silenced tunes.

On the lawsuit itself, Foley says it's unfortunate that it had to be filed ... since he claims Peloton was in talks with at least a few of the publishers before they pulled the trigger.