Jackson is sidelined with a hamstring strain, while Emerson Thome has suffered a setback in his recovery from injury.
It has left Ian Breckin as the only recognised central defender, but Wright's versatility will fill the void.
Primarily a right-back, the former Crewe player replaced Jackson during last week's win against Ipswich and caught the eye when coming on as a sub with a dominant performance.
Fringes
Latics manager Paul Jewell said: "One of the positives last Saturday was David Wright.
"Wrighty was one of our better players and I knew he could play at centre-back as I'd seen him do it for Crewe.
"I've been saying to players who are perhaps on the fringes that this is the time of the season when we need everyone.
"This is not the time for people to feel sorry because they are out of the picture.
"All of a sudden, someone could get their chance for one reason or another and they need to be ready for it."
Wright started the season as a regular following his summer transfer from Crewe before losing the battle for the right-back slot to Nicky Eaden.
His last league start was on November 20 against Leicester, although he did feature in the FA Cup at Derby in January.
Being able to play Wright in the centre of defence has brought Jewell some vital time as he weighs up the fitness of Jackson and Thome.
Jackson's hamstring strain is not thought to be too serious and he could be back in contention for the games at Brighton and Nottingham Forest next week.
But Thome has been out of action for a month, first with hamstring trouble and now with a calf strain.
Jewell could therefore be reluctant to let the March 24 transfer deadline pass without bringing in cover at the back.
He said: "We don't want to be left short after the deadline.
"We have three games coming up and then a fortnight's break, which might give the injuries time to clear up.
"But if we pick up any more injuries in the coming games, we might have to get another centre-half in.
"Jacko has nicked his hamstring, which is strange because it is normally a sprinter's injury, while Emo had a hamstring problem but has now aggravated his calf which is affecting his rehabilitation."
Also keeping the treatment table warm is midfielder Alan Mahon whose knee injury continues to be a worry. He has missed the last three games with a cyst inside his left knee and is unlikely to be fit for the visit of Millwall.
Jewell said: "The cyst keeps filling up with fluid – one day he is okay, the next he's not.
"It's a difficult one and we're sending him to see a specialist to see if we can get it sorted."
But there was better news concerning Nathan Ellington.
He twice dislocated his shoulder in recent days – once when he rolled over in bed, but he was able to train with the squad yesterday, and bar any setback in training tomorrow, should play on Saturday.
The visit to Nottingham Forest a week on Saturday is all-ticket. Seats went on sale to season ticket holders today.
The West Ham match on April 2 at the JJB is all-ticket for both sets of fans.