The film, which stars Mark Wahlberg and a teddy bear voiced by Seth MacFarlane, made $32.9m (£20.9m) between Friday and Sunday, according to studio estimates.
Jurassic World and Inside Out made $54.2m (£34.5m) and $52.1m (£33.1m) respectively over the same period.
Canine drama Max, another new release, made its bow-wow in fourth place.
The film, about a military dog afflicted with post-traumatic stress disorder (PTSD), made $12.2m (£7.7m) in its first three days in North American cinemas.
Ted 2's opening weekend tally is no disgrace for a film rated R, which requires under 17s to be accompanied by an adult parent or guardian.
Yet the Universal release had been expected to perform better given the success of its 2012 predecessor, which took almost $550m (£350m) at the worldwide box office.
"We could have had a higher gross, but we get the gross we get," said Universal's Nick Carpou. "It was a very competitive marketplace this weekend."
Jurassic World, which was also produced by Universal Pictures, has now spent three weekends as the US and Canada's number one film.
The fourth instalment in the resurrected dinosaur franchise has now made more than $1 bn (£637m) at the worldwide box office.
Ted 2, in which the title character tries to convince a court he is a person so he can have a child with his wife, opens in the UK and Ireland on 8 July.
Inside Out, an animated feature in which much of the action takes place inside a young girl's head, makes its UK and Ireland debut two weeks later.
The full US and Canada box office top 10 is as follows.
Comedy sequel Ted 2 has failed to knock Jurassic World off the top of the US and Canada box office chart, opening in third place behind Pixar's Inside Out.