The 21-year-old midfielder had only just come back into the U's side after several months out following ankle surgery in January but left the pitch after just nine minutes.
He had gone in for a challenge with Crewe striker Chris Dagnall and conceded a foul, but landed heavily and limped off the pitch.
Szmodics was then stretchered down the touchline and taken straight to hospital for an x-ray.
And he later confirmed that the scan had showed a break in his leg.
Szmodics said on his Twitter account: "Gutted to break my leg in today's game.
"Thanks for all your supportive messages.
"They mean the world to me.
"I'll be back stronger."