Arnold Schwarzenegger -- I'll Terminate Nutrition Company -- With $10M Lawsuit

Arnold Schwarzenegger is threatening to crush the company he says jacked his image to sell cheap nutrition products ... according to a lawsuit obtained by TMZ.

Schwarzenegger claims the Arnold Nutrition Group slapped his name and photo all over its products -- things he would NEVER endorse because they haven't been subjected to rigorous testing.

Arnold makes it clear in his lawsuit ... nobody gets his endorsement unless he BELIEVES in the product ... and unless he gets paid for the full value of his name and reputation.

Arnold says the company is defrauding the public. He wants at least $10 mil ... but he hasn't asked for a total recall. Yet.