Bates limped off in the early stages of last weekend's defeat at Crystal Palace and despite hopes he would make a quick recovery, Boro face a lengthy spell without their captain.
It will be a big blow to Mowbray, who handed Bates the captain's armband in January before Gary O'Neil departed for West Ham United.
Bates' injury means the Boro boss will have to pick his central defensive partnership for tomorrow's Championship clash with Swansea City from Seb Hines, Jonathan Grounds and new boy Max Haas.
Grounds, who recently returned to the Riverside after a loan spell at Hibernian, replaced Bates and partnered Hines in the defeat last Saturday, and it is likely Mowbray will go with the pair again.
"When I first came here Wheater and Bates were the centre-halves and we looked very solid defensively," the Boro boss said.
"A few weeks down the road and both are unavailable.
Of course they're both big losses but I've always said it's a opportunity for somebody else.
"At the moment the opportunity is there for Jonathan Grounds and Seb Hines to try and do the job and they'll have competition over the next few weeks from Max Haas as he acclimatises to the league.
"I don't think he (Grounds) did anything wrong last weekend.
Matthew came off with his hamstring injury and I think he was the more obvious choice to play because he's more experienced in the English game and I couldn't fault him really.
"Matthew is a loss to any team with his experience, mobility and strength but Jonathan came in and did fine and there's every chance he'll be given the opportunity to build on last week's performance.
"Matthew's been great since he took over the captaincy but injuries are part and parcel of football and we just have to deal with them.
If we lose on Saturday I cant say we're missing Wheater and Bates, you have to put a team out there that can try their best.
" New boy Haas made his first appearance in a Boro shirt when he completed 70 minutes for the reserves on Wednesday night.
However, Mowbray is reluctant to throw the former Bayern Munich II defender straight in and is keen for the 25-year-old to play more reserve football before making his first-team debut.
"He was brought here because we can see his attributes and his physicality regarding his man-to-man defending talent," Mowbray explained.
"He's comfortable with the ball and fits the criteria for what we like in a footballer.
"The German league is a slower tempo and different type of game and I think the boy needs a spell to watch and see what it's all about.
"It would be ideal for him to play some reserve football and train everyday and get used to it then he might get a chance in the first team.
" The Boro boss is also hoping Joe Bennett will recover in time for tomorrow's game after he suffered a dead leg while making his England Under-21 debut on Tuesday night against Italy.
Barry Robson and Marvin Emnes are both back training, as are long-term absentees Willo Flood and Rhys Williams.
Mowbray's other new signing, Moroccon midfielder Merouane Zammama, is also in contention but it is likely he will start on the bench.
The former Hibs man trained with his new team mates for the first time yesterday after gaining his international visa, but like Haas, Mowbray is keen to slowly ease him in to English football.
"As a young human being in the dressing room he's a great addition.
" Mowbray said.
"He's a footballer and a very talented one.
He's got two wonderful feet to dribble and skip past people and good pace.
"He's more of a creator than a goalscorer and I saw it as too good an opportunity to turn down with his contract coming to an end at Hibs.
I signed him five years ago at Hibs, he's a talent and it's how he adjusts to the league.
"We'll see how he goes over the next few months.
Hopefully he can acclimatise pretty quickly and can be a benefit to the squad.
"
Source: Northern Echo
Source: Northern Echo