Baffled players stood and watched before Zurich defender Loris Benito gave chase and managed to rugby tackle the animal which bit him on the finger.
The pine marten slipped away but was eventually caught by goalkeeper David Da Costa who handed it to stewards.
"In hindsight, I was probably a little foolish," Benito told Swiss television at half-time. "You don't know what sort of disease it might be carrying. It was painful."
They had Vullnet Basha sent off for a second bookable offence five minutes before halftime. Gattuso became Sion's fourth coach of the season when he was appointed last month.
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