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.

The 59-year-old spent last season at the Daggers under boss John Still, whom he worked with at Luton.
Harris has become Wood boss Luke Garrard's number two on an undisclosed-length contract.
"I can bring experience with me because I have been very fortunate during my time with John Still," Harris said.
He added to the club's official website: "If you are a number two then you are the eyes and ears of the players and you certainly have an input into the coaching side and an input into the game management side and, as I said, I have been fortunate in the clubs that I have been with.
"With Dagenham, for instance, we got out of the Ryman league and then we got out of the Conference, as it called then, and we then took Dagenham into League One in the Play-off final against Rotherham."

Training has been fairly intermittent for me recently due to a torn ligament in my big toe after blocking a shot at Accrington a few weeks ago. Painkillers and anti-inflammatory tablets have been a necessity to continue my season, so I totally understood the manager's decision for me not to start the game.
The game against AFC Wimbledon the week before had been disappointing, and playing through injury is tough enough, but when results go against you it magnifies any weakness that you have.
We were 1-0 down at York when I got the call to go on. Coming on at that scoreline is obviously the scenario where you are desperate to help your team score the equaliser.
I had scored a few during the week in training, so I had a positive mindset when I entered the field of play.
Anthony Stewart hit a shot from just inside York's penalty area and I took a chance on the goalkeeper palming it towards me. Thankfully that was what happened and I was able to dive at the ball and head it in for the equaliser.
At the same time, a York defender tried to volley the ball clear but I was able to get there first. Unfortunately for me, the York defender connected with my arm instead of the ball and a further twist is that the player in question, Dave Winfield, is a really good friend of mine.
Midway through the celebration I suddenly realised that my arm was extremely painful. I tried not to give it too much thought, though, as the only thing I could think about was not losing the point that we had just earned for ourselves. There was also the chance that we might be able to snatch a late winner.
The pain was starting to really intensify but we had used all of our substitutes, so the option of going off had been taken away.
There was no way that I was going to leave my team-mates with 10 men whilst I was still able to run so I just had to grit my teeth and get on with it.
Plus, although it was extremely painful, I did not realise that it was broken and the last thing I wanted to do was walk off with a bruised arm!
I was so relieved when the referee blew the final whistle and I could not wait to get off the pitch.
I headed straight for the Royal Berkshire Hospital as soon as we got back and left there at four o'clock in the morning with my arm in a cast. I had broken the ulna bone in my right arm and it might have finished my season.
I spoke to Dave both after the game and again on Sunday. He feels bad but we are adults playing a contact sport and these things happen. He did not mean for it to happen.
I am now fairly useless at home as I am unable to help my wife with my daughter. I hate not being independent so it is driving me mad. Missing games at this time of the season is going to be horrible - it is bad enough at any time, but especially during the run-in.
Finally, I would like to congratulate Northampton on their promotion to League One. In Ricky Holmes, they have one of the players of the season and someone I put into my team of the year. Northampton are the best team that we have played and fully deserve their promotion.
A teenager has been arrested in connection with an alleged hit-and-run incident which left a boy in hospital.
[NEXT_CONCEPT]
National League side Boreham Wood have named former Luton, Stevenage and Dagenham coach Terry Harris as the club's new assistant manager.
[NEXT_CONCEPT]
I have been involved in some incident-packed match days and seen most things during close to 12 and a half years at Wycombe Wanderers, but breaking my arm while scoring in Saturday's game at York City was a new one - even for me.