If economic growth is defined simply in terms of tons of refined resources pulled out of the ground, then yes, of course economic growth has a limit. Trivially so.
If economic growth is defined as providing people things they want, a definition that normally makes economics make much more sense, it becomes much fuzzier. What is the "economic value" of an SD card loaded down with the entire run of the Simpsons and Friends? What is the "economic value" of an MP3? What is the "economic value" of knowing how to run a boarding school successfully? There's no obvious upper limit to how many desires could be satiated, especially once you get away from brute material concerns like food and water. If you're willing to go sci-fi, and let machines and perhaps simulated humans have desires that the economy could satisfy it becomes even harder (and as we already let "companies" have such desires it's not really that far a journey from where we are), and it was already pretty hard.
(Note I'm not saying there are "no" limits in that case, I'm saying they become a lot harder to define, and much, much harder to defend. If there are limits, but we can't reach them by the end of a the longest lifetime a baby born today will live for, it's not particularly clear that our opinion has any meaning or force. The economy of 2132 will still have physical constraints but I wouldn't care to guess a whole lot about its nature and how "large" we would consider it to be versus today's economy. For that matter, how "large" is the 2022 economy versus 1822? It's a lot harder a question than meets the eye.)