I've 66% in 10th, 44% in 12th and 52% in degree. I'm planning to do MBA in finance. Will this marks affect my placement after MBA?

Yes, it will affect as companies see previous records of academics.

For top tier companies, it may affect because in most of the top companies, they candidate should be in 1st class criteria from 10 till he completes his Mater degree then only he will be qualified to for interview.

Yes, in most of the good companies they set the minimum of 60% to appear for their entrance test, but not everyone. I would also say that if you are good with your communication skills and technicals, then you might not have to face many difficulties. So, work on your soft skills if you want to ente

Some companies will hire on the basis of exam, group discussion and personal interview some will ask your scores in your previous education but if you do MBA from any good college, then you will face less difficulties at the time of placement.