The 33-year-old, who joined the club on a one-year deal on the eve of the season following a successful trial, suffered the injury in the first half of last Saturday’s draw at Rochdale – just his second outing for Rovers.
It is another cruel development for the centre-half, who suffered a double leg fracture in his pre-season debut for another one of his former clubs in Middlesbrough in a friendly at York in the summer of 2015 – and played just one competitive game for Boro.
Moore said: “Alex is going to be out for a lengthy period of time. The scan results have come back and declared that he has ruptured his Achilles and all our thoughts are with Alex.
“We will get him back on the road and he is due to have surgery in the next couple of days and then he is on the road to recovery.
“It is bad news. He had played in the last couple of games and I thought he had done really, really well. He will be sadly missed and we wish him a speedy recovery.”
On potentially bringing in another defensive option, he added: “It is another area we are looking at again in terms of going forward. We may have to look at strengthening that area again.”
Rotherham United’s scheduled League One home game with Bury on Tuesday has been suspended.
It is the fifth successive game to be called off for the financially-stricken Shakers.
The suspension comes as the League One club works towards an August 23 deadline to avoid expulsion from the EFL, who are awaiting evidence that the Shakers can pay creditors and have funding for the season ahead.
Rotherham United loan forward Carlton Morris is unlikely to be available for the next fortnight after suffering a head injury in the midweek Carabao Cup win at former club Shrewsbury.
Manager Paul Warne, who is chasing a centre-half and two new wingers before the September 2 transfer deadline, said: “I spoke to him, he is alright, but with the protocol to protect players these days which is essential, he is not going to be available for two weeks.
“That is what I am led to believe, unless I get good news that he has passed some of the protocol.”