Paterson was carried off on a stretcher after twisting his knee during the club's 3-1 Petrofac Training Cup win over Alloa on Saturday.
The club feared cruciate ligament damage but Paterson has been given a less daunting diagnosis of a damaged cartilage.
Neilson told Hearts News: "We had Callum looked at and, once it was realised that the injury wasn't as bad as we first thought, went ahead with surgery.
"The operation - a medial menisectomy - was a tidy-up job which went absolutely fine. Because of the nature of the injury, we believe Callum will return to the training field in around a couple of months.
"It's still an injury that will keep him on the sideline for the foreseeable, but because we could've been looking at six months out or longer, it's a huge relief that it isn't as bad as that.
"Callum will start his rehabilitation straight away and I'm sure he will come back stronger and better than ever."