It's the same right hip that Pitta fractured and dislocated last summer, an injury that cost him much of 2013.
The nature of the injury brings into question whether Pitta's playing career is now in jeopardy.
"I don't know the ramifications of that long term," Harbaugh said. "I'm going to be really hopeful for Dennis' return and I'm sure we'll learn about that in the coming weeks."
Pitta, 29, entered Sunday tied for the team lead in receptions. The former first-round pick signed a five-year, $32.5 million contract in February, a deal that included $16 million guaranteed.
"We're looking for another tight end," he said. "We've been working on that right now upstairs. We'll see if we can bolster that position as well."
Jermichael Finley and Dustin Keller are two notable tight ends on the free-agent market, but both come with significant health concerns.