If you are just paying the minimum payments on your Credit Cards it will not necessarily negatively effect your FICO score. The credit bureaus don't know how much you are paying month-to-month, but they do know your balance in relation to your available credit. If you are just paying the minimum payment on your credit cards, then chances are that you are unable to pay your balance down.  A higher balance, then negatively affects your FICO score. 

As a rule of thumb, we used to tell our borrowers that paying down Credit Card balances was the easiest way to proactively push your credit score up. People would assume that since they were always paying on time, even if it was only the minimum payment, that their credit would be unaffected.  The truth, however, is that the Credit Bureaus want to see your balances at less that 30% of your available. A highly leveraged borrower is at a much greater risk for falling behind. 

So, long story short, try and pay more than the minimum payment, but don't pay off your credit cards and then close the account.