The British musician was with his dad, also named Tom, in a parking lot in Leicester, England in May (14) when the freak accident happened.
Meighan, who does not have a driving licence, accidentally pressed the accelerator pedal and knocked him down, and Tom Senior was admitted to hospital to treat minor injuries.
A source tells Britain's The Sun newspaper, "It was a bizarre accident and Tom feels really bad about it... He was in a car park with his dad when it happened and was asked to release the handbrake to let the car forward slightly... by mistake, he put (his) foot on the accelerator and went into his father. Tom Senior was badly bruised and had a few stitches and spent a day in hospital but he knew it was a complete freak accident... Tom himself felt awful about it all but thankfully his dad has made a full recovery and saw the funny side."
The accident happened just weeks before the band is due to play a career-defining headline set at Britain's Glastonbury festival next week (beg23Jun14).