McCartney crossed the whitewash in the second half to give Treviso a mountain to climb as they tried to get back into the match, driving over after a brilliantly-worked line-out, but was forced off just a minute later.
And with the likes of John Cooney and Matt Healy also out injured, Connacht will take a depleted side into their first European outings of the season this weekend.
"Tom McCartney suffered a hamstring tear scoring his side's second try on Friday night. The 30-year-old hooker is expected to be unavailable for up to six weeks," said a Connacht injury update.
"Scrum-half John Cooney will also see a surgeon this week to examine the extent of a shoulder subluxation.
"Matt Healy, who ran in the province's third and final try against the Italians, is unavailable this week having incurred a joint sprain to his hip on Friday.
"Nathan White was concussed during the first half of Friday's game and subsequently removed from the pitch. The Ireland prop had mild symptoms and will continue to follow the return-to-play protocols.
"Meanwhile, second row Quinn Roux had surgery last week to repair the nasal fracture he suffered in the recent home win over Edinburgh. He is expected to return to action in three weeks' time."
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