No, and maybe just the opposite. Technique problems cause injuries more often than equipment woes, but racquet weight can be an issue, but it works differently than you might think.
Mass is a great shock absorber, and a lighter racquet will not “defend” against the ball very well, especially if you play against people who hit hard. A heavier, more head light frame will have a higher “recoil weight”, which would keep it from “kicking back” in your hands (which is especially valuable at net if you’re a doubles player). You can add weight at the 3 and 9 o’clock positions in the head if you need more torsional stability, which is a common customization move.
It is possible to use a racquet that is too heavy, but the opposite is much more common. We could check your racquet’s specs against your style of play to get the answers you need.