the Xinjiang place on the corner of Xikang Lu and Wuding Lu is my favorite...the sauteed lamb w/ cumin is particularly good, and the upstairs area has comfy booths...i'm not sure the name, but it's a famous place and it might just be called "Xinjiang" in English...easy to spot on the (SW side of) that corner, w/ the big sign and the kebabs being grilled out front...
Not to be obstructive, but Shaanxi (陕西) and Shanxi (山西) are two different provinces.
They are right next to each other, but there might be some differences to consider.
Shaanxi is the province where Xi'an and the terra cotta warriors are located, and Xi'an at least has a fair amount of Muslim/Uighur population.
Shanxi had a scandal involving slave labor and brick kilns a year or two ago. I'm not sure what they're famous for food-wise, apart from vinegar.
The Uighur restaurant on Fumin Lu, south of Julu Lu, is okay. It's on the West side of the street, has a blue awning & a kebab grill out front. I think it's called Uighur Restaurant or something like that. I've also been to a restaurant on Yishan Lu near Xujiahui that was pretty good.
To be a bit more constructive, there's a Shaanxi (i.e. the province with Xi'an) Business Hotel on the North side of Yan'an Lu, just East of Maoming Lu - Yan'an Zhong Lu #658. (上海市静安区静安区延安中路658号) Telephone number +86 21-52624866. According to the internet, it's managed by the Shaanxi Provincial Government's Tourism Board, and has at least one restaurant. I've walked by the place a few times, and thought they had a sign up saying they're also the location of the Shaanxi Provincial Government's Rep Office in Shanghai, although the internet claims that said rep office is actually located on South Suzhou Road.
So you might be able to get authentic Shaanxi food there, with the following caveats:
1) Although I have tried to find provincial rep offices in Shanghai to eat other regional foods, i.e. Hunan, Yunnan, I've never actually made it to one of these rep offices to do so. Although I think another poster had some good things to say about the Hunan Rep Office's restaurant. And "state-run" is not always synonymous with "high-quality." It's actually not always synonymous with "sanitary" or "edible." So your mileage may vary.
2) I'm not sure what type of Shaanxi food you're looking for - are you craving Uighur kebabs? In that case you might be better off looking for specifically Uighur places or the Xinjiang Autonomous Region's rep office. Other commenters have pointed out that Lost Heaven provides the food of Yunnan's minority tribes, whereas Southern Barbarian is more the food of the Han people who live in Yunnan. I'm not sure if there's such a distinction to be drawn in Shaanxi, or if there is, where the Shaanxi government's tourism agency would come down on the issue.
If you're really all about the vinegar (Shanxi), you could try checking with their rep office, which, according to the internet, is located in Hongkou District, on Zhongshan Bei Yi Lu, # 1250, Bldg. 5, Room 702. (上海市虹口区中山北一路1250号沪办大厦5号楼702室). The phone number listed on the internets is 0216542731, but that doesn't have enough digits, so I'm not so sure.
Good luck. Let us know how it goes.
There is the Friday Muslim market in Shanghai, it has all the traditional foods, but the versions found there are pretty universally considered mediocre at best. There was a fairly small local Xinjiang spot near where I used to live, across from the World Union Survice apartment, on Urumuqi Rd (a good sign?), a few minutes from Jingan Temple. It had all the usual Xinjiang fare and did a great job on them and all the staff were Uighur.
Sapar is the one around Urumqi Rd. I've only had a couple of dishes there, but I thought the food was pretty decent to warrant a return. But I guess it helps that I own a house nearby...
Entry on Dianping: http://www.dianping.com/shop/2335114