The Mudd Incident was an event in which the USS Enterprise was involved in early 2259, during which the crew confiscated a K'normian trading ship. A month later, Captain James T. Kirk used this ship so his landing party could pose as arms dealers while infiltrating Qo'noS. (Star Trek Into Darkness)
The "Mudd Incident" was conceived by Star Trek Into Darkness screenwriters Roberto Orci and Alex Kurtzman. When explaining where the name came from, Kurtzman stated, "It's kind of necessity is the mother of invention. We knew that for the mission that Kirk wants to go on to work, it couldn't be a Federation ship. So why the hell would the Enterprise have a non-Federation ship on board? 'I got it! The Mudd incident!" Given the fact that the name constitutes an in-joke referencing Harry Mudd, Orci admitted, "I still have a giggle about [writing that line] now." 
In the comic book Star Trek: Countdown to Darkness (co-written by Roberto Orci), the Mudd Incident took place just prior to the Enterprise's mission to Nibiru; Kirk uncovered a civil war on a pre-warp world where the aggressors were being given weapons by the Klingons, while the resistance were aided by Robert April and Mudd (β), the half-Bajoran daughter of Harry Mudd. Mudd's ship and its cargo were brought on board by Uhura, who had the command chair. Following a failed attempt to capture the Enterprise and deliver it to the Klingons, Kirk declared his intention to keep Mudd's ship aboard as it "might come in handy" while Admiral Pike ordered him, per Admiral Marcus, that April was to be delivered to Starfleet Intelligence and any further mention of April or his actions was strictly classified.