A new temporary west stand, which will provide around 4,200 seats is currently being constructed and will stay in place for the Glasgow 7s, which is being held at Scotstoun on 4 and 5 May.
More than 4,000 tickets have already been sold for this game, which is the Warriors final scheduled home fixture of the season.
Glasgow are currently top of the RaboDirect PRO12 and are hoping to secure a play-off spot, with just three games remaining.
Work on the Scotstoun pitch has also started this week, with some areas being re-turfed ahead of the Ospreys game and the Glasgow 7s.
Advance tickets for the seated west and north stands are priced at £20 for adults, £15 for students and senior citizens and £5 for under-18s. There are also limited tickets available in the main stand, which is priced at £25 for adults, £20 for students and senior citizens and £5 for under-18s.
Tickets for Glasgow's final scheduled home game this season against Ospreys on Friday 19 April (ko 7.35pm) are available now from the ticket office on 0844 800 3490 (Monday – Friday, 9.00am – 5.00pm) and online here