The governing body’s decision means the Ferrari driver retains his 14-point lead in the Drivers’ Championship heading into this weekend’s Austrian GP.
The FIA said in a statement Vettel had “admitted full responsibility” and “extended his sincere apologies to the FIA and the wider motorsport family.
“In light of these developments, FIA President Jean Todt decided that on this occasion the matter should be closed,” it concluded.
Vettel admitted he had over-reacted after running into the back of Hamilton’s car behind the Safety Car in a statement released on his website.
“With hindsight, I don’t believe he had any bad intentions. In the heat of the action I then overreacted, and therefore I want to apologise to Lewis directly, as well as to all the people who were watching the race. I realise that I was not setting a good example,” he said.