My understanding is that Apollinaire was arrested first, and implicated Picasso, who was arrested a few days later. But both were released after about a week.
The late John Richardson outlined the story in his biography of Picasso, v. 2. Picasso was in the midst of his movement into Cubism , and had gotten very enthralled by African and primitive art. Security at the Louvre was lax, and a man who had been a secretary to Apollinaire was stealing things and re-selling them. Picasso got a couple of sculptures. The thief started talking to a newspaper, and while he didn't name names, he said that one of his customers was a painter. And he mentioned a literary name that could be traced to Apollinaire. When the Mona Lisa was stolen, the police went after them all. Apollinaire confessed, Picasso was arrested. But they did not have the Mona Lisa.
You can also read the story here. But it's also a good excuse to read Richardson's Picasso books, which are excellent.