The pair featured in Sunday's draw with Arminia Bielefeld, but were both rested for Wednesday's defeat to Hannover 96.
With the central defenders having only recently returned to training following serious injuries, Black Cats boss Bruce is keen for the pair not to overexert themselves in a bid to prevent any recurrences.
After playing in Sunderland's first three pre-season games, Bruce felt it was especially important to give Bramble a rest after the 29-year-old missed a big chunk towards the end of last season with a knee injury.
Turner also returned from injury recently, and with new signing John O'Shea set to miss most of the remaining pre-season games, Bruce will hope Bramble and Turner can come through unscathed.
Republic of Ireland international O'Shea lasted just 34 minutes of his Black Cats debut against Arminia Bielefeld when he was forced off with a muscular strain.
Bruce had hoped to have the 30-year-old back for the final game of the tour tomorrow, but the Black Cats boss revealed the versatile defender could be out for a further two weeks.
He said: "It's disappointing that John hasn't played here (in Hannover), but we have still got three weeks left.
"We need him to be ready in a few weeks' time, not now. We have got games when we get back.
"It would be nice to see him play, but he got his leg in a difficult position against Arminia Bielefeld on Sunday and strained a muscle.
"We will have to keep an eye on how he is. The last thing we want to do now is risk anybody. If they have got anything slight, I would rather them give training and the games a rest."
Meanwhile, yesterday brought speculation linking Black Cats defender Anton Ferdinand with a return to former club West Ham United.
Ferdinand spent six years with the Hammers before moving to Wearside in 2008, but it is thought new boss Sam Allardyce is weighing up a move to bring the 26-year-old back to East London.
After the arrivals of Wes Brown and O'Shea, as well as the return to fitness of Bramble and Turner, Ferdinand could find himself pushed down the pecking order at the Stadium of Light this season.