The Serbian was not in the 19-man squad that boarded a plane bound for Bangkok on Wednesday, as the Reds kick off Tour 2013 presented by Aon.
The defender is likely to join his team-mates on the trip at a later stage, however, with United scheduled to play further games in Australia, Japan (x2) and Hong Kong before returning to the UK at the end of July. A match in Sweden will then follow on Tuesday 6 August.
"It's nothing serious," a club spokesperson told ManUtd.com. "Nemanja has a touch of sciatica [pain stemming from nerves in the back] and may still join the tour at a later date.
"In the meantime, he'll continue his pre-season preparations in Manchester at the Aon Training Complex."
United's first pre-season game is against a Singha All Star XI on Saturday 13 July (14:00 BST).