Zoe Bremner died at Dundasvale Court, Cowcaddens, in the early hours of Sunday following a party.
Police had earlier said her death was being treated as unexplained but drug use was one of the lines of inquiry.
The teenager has been detained in police custody and is expected to appear at Glasgow Sheriff Court later.
A 16-year-old man has been arrested in connection with drug offences following the death of a 14-year-old girl at a flat in Glasgow.