Dears,
Which online MBA is better for Entrepreneurship specialization taking into consideration the below criteria:

* Within the budget of 25K USD
* Doesn't require a GMAT?

I don't understand why you'd want an *MBA* with an entrepreneurship specialisation. Why not a certificate, diploma, MicroMasters or other masters?
See Specialisations often don't matter http://bit.ly/speMBA 

Thanks, Duncan, much appreciated.
I am looking forward to having my own business (part of our family business) within 5 years, I never thought of taking a master, I was focusing all the time on getting an MBA. Your words made me rethink again.

Any recommendation for an online masters in entrepreneurship? 

I suggest you use the search a bit and then come back with more specific questions based around your needs. It might not be a masters' degree. Try, for example,
- https://find-mba.com/board/europe/best-master-programmes-in-entrepreneurship-eu-50592 
- https://find-mba.com/board/uk-ireland/best-masters-for-entrepreneurial-study-65289
- https://find-mba.com/board/general-forum/most-valuable-mba-for-entrepreneurship-66525