Without the foal suckling the mare will automatically dry up - it will take time and it may take longer as they are next to each other (mentally the mare will still think she might need to feed her foal - just the way nature works!) but she will dry up in the end. Our mares are all at grass 24/7 and when we wean we do nothing extra except return the mares to fields that are well grazed down rather than the 'lush' fields they are on with their foals. Some mares can take up to a month to dry off, but after the first week there is an obvious sign that their udders are decreasing. Luckily we have plenty of space so our filly foals are not returned to the mare herd until the following year, but without exception, they all recognise their dams and with the generations that we have here, I will often visit the fields to find a mare happily grazing with all her daughters close by. I did have one filly who, when put back in with her dam a year after weaning, rushed to Momma and shoved her head straight under for a drink - she was met with a heafty kick and never tried again! LOL!!
All mares (and foals) are different and time is really the only answer. If, after you are happy that your mare has completely died up, you put them back together and your foal tries to suckle, then you may have to part them again for a bit longer. If, on the other hand, the mare tells her daughter in no uncertain terms to 'clear off' then you may be alright, but keep a good eye on them as a foal can be very persuasive and your mare might give in and possibly regenerate her milk supply.
Good luck!