World No. 1 Murray fell 6-2, 6-4 to Italian Fognini in their second round clash late on Tuesday night.
Murray, who turned 30 on Monday, continues to struggle for consistency on his return from an elbow injury, having reached the semifinals in Barcelona only to then be knocked out of the Madrid Open by Croatia's world No. 41 Borna Coric.
The partisan home crowd were delighted when world No. 29 Fognini broke Murray in the opening game and went on to take a 3-0 lead, before closing out the set 6-2 with a love service.
Murray found himself under immediate pressure in the second set, when his serve failed again as Fognini opened up a 4-1 advantage.
There was a brief recovery by Murray as a break and a hold saw him trail 4-5. Fognini, though, maintained his dominance to serve out victory and secure a first win over a world No. 1.
"I am just not playing well," Murray said in his post-match press conference.
"I mean, the last couple of weeks, they have been tough and I haven't played well.
"I am just not playing good tennis and I need to try and work out how to turn that around."
Information from the Press Association was used in this report.