Battery replacement on MacBook Pro 13" Early 2011 considerations
No. This A1322 model battery fits many MBP 13's, all the way back to 2009 version. Given the number of iterations and countries MBP have been sold, it's due to have different part numbers.

I also have a MBP 13' Early 2011 version. Two months ago I replaced the battery with a A1322 battery I bought online and I haven't had a problem.

Beware that:


If you are going to ifixit yourself, taking out the battery requires a special screwdriver. I got mine as a free addon from the vender.
Download CoconutBattery. It's a free app that gives you information like manufacture date (which I cannot find under System Information) and charge cycles.