The former Rotherham man hobbled off the field 18 minutes into the game after winning some good headers and tackles.
He has been suffering with a foot problem recently and that slight niggle has so far kept him out of the games at York and against Birmingham.
But the fear is that the 25-year-old could have damaged his ligaments, and tests today will identify whether he needs to take an enforced lay-off.
Should Branston have to sit out any action at the start of the season, it seems as if there is a ready-made replacement in Patrick Collins.
The ex-Sunderland youngster, who was chased by Leicester and Crystal Palace in the summer, has been mightily impressive for The Owls and will grab any chance he gets with both hands.
Graeme Lee limped off against Birmingham but should be fit for the Everton game on Tuesday night while Lee Bullen can also come into the centre of defence to lend a helping hand.