The 29-year-old, who has netted 15 times this season, sustained an injury to his quad and was withdrawn after 80 minutes as the Millers were beaten by MK Dons.
It follows a more serious injury to fellow forward Will Grigg last month, with the Sunderland loanee likely to be out until the end of the season.
An initial assessment of Ladapo's injury would see him miss league games against Wycombe Wanderers, Lincoln City and Shrewsbury Town as well as Wednesday's Papa John's Trophy semi-final tie at Hartlepool United.
"Freddie looks like he is going to be out for a couple of weeks, potentially," confirmed Warne.
The trip to Hartlepool could see Warne hand a debut to Georgie Kelly, who has been improving his fitness since joining Rotherham from League of Ireland side Bohemians, where he was in a part-time environment.
Saturday's defeat to MK Dons may change Warne's plans for what team he fields on Wednesday.
The game could see the returns of Rarmani Edmonds-Green and Mickel Miller, who have both been sidelined by hamstring problems.
"It might change my thought process for Wednesday night as we need a good performance and we need a win," added Warne.
"I need the same thing at Wycombe. Going to Hartlepool on a Wednesday night is not an ideal fixture for us but I respect the competition. We are going to have to look at who is fit and ready."