The England international injured his knee playing for England Sevens at the World Cup in Hong Kong 10 days ago and was ruled out of last Saturday's win over London Irish.
Paul is set to be out for between six and eight weeks and will be unavailable for Gloucester's final three Zurich Premiership games, and any play-off matches.
Commenting on www.gloucesterrugbyclub.com Melville said: "It's a set-back but in some ways sums up our season. We have just had so many people injured at crucial periods, but you only have to look around the Premiership to see that other clubs are in a similar situation."
Commenting on www.gloucesterrugbyclub.com Paul added: "It's a big disappointment. I'm concentrating on getting back to full fitness, and will be right behind the rest of the team as we push for the top three slot in the Premiership and next season's Heineken Cup."
Paul, who has missed only a handful of games in four seasons with Gloucester, will see a specialist next week who will assess whether an operation is required.
Despite the injury, Nigel Melville's fly-half options could be boosted for Gloucester's next Premiership game at home to Leeds Tykes on Saturday 9 April with the return of Duncan McRae.
The Aussie stand-off has had an injury hit season, with his most recent knee injury ruling him out since the defeat away at Quins at the beginning of February.
As well as McRae's possible return, 22 year-old Brad Davies, who played the full 80 minutes at number 10 for Gloucester in the 13-12 win over London Irish on Saturday, was in commanding form for Gloucester against the Exiles at the weekend.
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