Not sure where you're based, but most games companies will ask for a degree in Software Engineering or Computer Science. Here in the UK, there are a number of games specific software engineering degrees. Decent ones are generally well received by the industry.
Any games course worth its salt will have a heavy dose of maths and/or maths entry level requirements. Best to take a look at the syllabi and see what's on offer.
You can be Masters in Computer Science and know very little of C++. You can have high school as your highest degree, and know C++ very well.
Degree isn't equal to knowledge. You may finish any university you want, but if you're not willing to learn, if you're not learning for yourself and you're not extending your knowledge - no degree will help.
So if you want to join gaming company, learn C++ and write games. There's no better way to become game programmer then to program games.
PS. But if you're looking at what degree may help, than most companies will look for Bachelors degree in Computer Science, or equivalent.
Go to the site of companies you would like to work for, search for the job offers, and see what they want you to know.
Im based in the USA my college right now offers a associates in computers and information taking general comouter classes while specializing in C++ then id tranfer to a different school to get my bachelors