The 14-year-old boy who was injured was walking with a 15-year-old boy when he was struck in Fernhill Road, near Rutherglen, at 14:15 on 24 January.
Police previously said a light-green Vauxhall Corsa mounted the pavement before heading off towards Castlemilk.
They have now arrested a 16-year-old male. He is expected to appear at Glasgow Sheriff Court on Monday.
A teenager has been arrested in connection with an alleged hit-and-run incident which left a boy in hospital.