My husband suddenly moved out without any warning and rented his own apartment. We have been married for 20 years with 2 children. Can he withdraw from his 401K without my knowledge or approval?

Yes, assuming that his plan allows it. If he is still an active employee he won't be able to make a withdrawal unless he can show that he needs the cash for one of the hardship purposes as defind by the IRS. If the 401(k) is with a former employer then he most likely can take a withdrawal, but he will have to pay income tax and the 10% early withdrawal penalty on it (assuming he's under age 55). I would suggest that you try and find any paper records that document what's in the account, because if this goes to divorce you have rights to some portion of his 401(k) account.

**EDIT** He can most likely take a loan from his current 401(k) if he wants, but only up to half its value. So he can't touch "your" half (if you are due that much as determined in your divorce proceedings).