Is Part Time MBA a good option for Masters for Programmer

It is always good to have sufficient qualification to get stand at platform to demonstrate your skills. You can't demonstrate your skills unless you get a chance and what if that is on the basis of educational qualification?

So, don't waste your so much time and go for higher education. Day by day our education level is increasing. Few years back, government stopped recruiting 10th pass candidates as clerk and increased the minimum qualification to 12th. 
Had you done engineering(BE/BTech), may it not required in future but for guys like you who has don B.Sc./ BCA are highly advised to earn their masters. MCA is taken equivalent to BE/BTech (don't confuse one is master degree and another is bachelor). So, for brighter future, you should go for MCA. Also, don't go for 1 year M.Sc in shortcuts (just getting master degree) as some education counsellor may misguide you for this.

Also, I would like to say, always prefer central universities. If you are unable then pick state universities(non-private). Picking private state university should be your last option.
Since, MCA is considered as technical course, it should be recognized by AICTE. (be noted that universities/institution highlight themselves that they are AICTE approved. Don't be in their word and check if particular MCA course is recognized or not. They may show you few months before, honorable court has said that AICTE approval is not necessary. But be careful.