The defender went under the knife last week and began his rehabilitation almost immediately.
He will spend the first weeks of his recovery at English Championship side Fulham, where his dad, ex-Celtic captain Peter Grant Snr, works.
Peter Houston explained: “Peter’s dad called me and we discussed things and he’ll spend the first few weeks at Fulham. They offered to take him for the first few weeks and I’m delighted with that.
“We have one physio here - Ross Grady - and he has a lot to deal with. At Fulham they have all the sports scientists, the Academy physios, first team physios, and all sorts of equipment that we don’t have at Falkirk, and that can only be a good thing for Peter.
“He’s down with his family, he’s in and around the right people so for one month getting the best of treatment and equipment maybe two or three times a day, it will hopefully aid his recovery. It’s a big help to me, and I was delighted to take the call from his father.
“He’s just as keen to see his son get back because he sees how well he’s done and how he’s improved. He’s looking at how he can get Peter back quicker, I’m looking to get him back for the start of next season.”
Grant tore his cruciate ligament at Livingston last month, but played the following week against Rangers at Ibrox before the scale of his knee problem was identified by a hospital scan.
Kevin McCann is also out with a medial knee ligament strain, but has resumed running in training this week.