Robertson will miss today’s League One visit of Blackpool because he is seeing a specialist.
With right-back Billy Jones also out, Warne says the Millers are “one injury away from bad news” but he is not planning a drastic overhaul with his side a point outside the automatic-promotion places.
“I am not getting too excited about this transfer window,” said Warne.
“Maybe we need some (defensive) cover and we are investigating that, but it won’t be something that happens in the next few days.
“If you do a massive change in January you must have got something significantly wrong in the summer.
“I would like to think we would get a couple in, but it depends on a chain.”
Robertson has been struggling with a groin problem for some time, and succumbed in Sunday’s first half against Peterborough United.
“I don’t think we’ll see much of him in January,” said Warne.
“We go from feeling in a good place to being one injury away from bad news.”
Joe Mattock starts a three-match ban for his red card in the 4-0 win over Posh.
Last six: Rotherham United WLDDWW; Blackpool WWDLLD
Referee: J Adcock (Nottinghamshire).
Last time: Rotherham United 1 Blackpool 0, May 5, 2018, League One.