The IRS doesn't have anything to say in this situation unless you also understate your business income. If your business is in any other form than a sole proprietorship, creditors or others with a stake in the business might take exception to having business income diverted to personal use, even by an owner.
Your bank probably has a policy against such deposits, but may have an exception for sole proprietorships. The business case for the bank's policy is that the bank could be liable if a creditor of the business claims that funds were diverted from the business and that you didn't have authority to divert them. If that creditor happened to be the IRS, the bank could be liable for unpaid taxes. If your business is a sole proprietorship and the bank won't accept the check for deposit to your individual account, deposit it to your business account and write yourself a check from there.
BankingQuestions.com is a free service made possible by the generous support of our advertisers. Advertisers are not responsible for site content. Please help us keep BankingQuestions.com FREE by supporting our advertisers. When you see an ad for a product or service you may have an interest in, click through to learn more.