The Indian, ranked 85, lost his first round 6-2 3-6 3-6 2-6 in two hour and 38 minutes to the Italian.
Yuki has now lost all his four matches against Fabbiano, ranked 133.
Yuki was the lone Indian competing in the singles but as many as six of his compatriots will compete in the men's doubles later this week.
The 25-year-old has featured in the men's singles main draw of all three Grand Slams of the season so far but is yet to win a match.
He had qualified for the Australian Open and earned direct entry into French Open and Wimbledon, courtesy his top-100 rank.