Do I have to claim investment income if I have not withdrawn any funds from my investment account?

[BobB7]

Yes you do.  Wait until you get the 1099 tax form from the bank/broker/fund.

[Hal_Al]

If you do not get a form 1099 (1099-Div, 1099-Int, 1099-B), you do not need to report any investment income.
Otherwise, dividends, interest, capital gains credited to you account are taxable, even if you didn't withdraw them.

Dividends, interest, capital gains earned in a tax deferred account, like an IRA, are not reportable and you will not get any 1099's for that activity.