The club are due to make an announcement regarding the scheduled home derby with Barnsley on December 29 and the trip to Cardiff City on January 2 later today.
The news comes following the postponement of Saturday’s home game with Derby County due to a positive Covid-19 test within the Millers ranks.
A further player tested positive and a number of other positive tests have since been recorded among the club's squad.
A club statement said: “Following a number of further positive cases of Covid-19 confirmed last night (Tuesday) within the Rotherham United first team squad, we have reluctantly – but with the safety of our players and staff at the forefront of our minds – informed the EFL and our opponents, Middlesbrough, that we will be unable fulfil our Boxing Day fixture.
“Paul Warne’s side were set to face Boro at The Riverside on Saturday 26th December 2020, but following an increased series of testing throughout the early stages of this week, brought about by the postponement of last weekend’s fixture against Derby County, the club have, following consultation with the EFL doctors, been left with no choice but to inform the EFL of our decision to rearrange the game against Middlesbrough.
“The club will continue to monitor the severity at which the virus has spread - alongside the health and well-being of our first team squad and those connected to them - whilst remaining in contact with our upcoming opponents and the EFL on the matter.
“We hope to make a decision on future fixtures later today as we continue discussions with the EFL, with whom we will work closely, to ensure the safety of everyone connected with the football club at the forefront of our minds."