The victim was attacked in a flat in Southdeen Road, Drumchapel, at about 00:30 on Tuesday 13 December.
Police issued an appeal for information at the end of December.
They have now said that a 31-year-old man has been arrested in connection with the incident. He is expected to appear from custody at Glasgow Sheriff Court on Monday.
A man has been arrested after a 32-year-old woman was seriously assaulted in Glasgow.