That's tricky. Probably not very much, although it depends on your overall situation. Paying debts regularly helps your score. Having open accounts helps your score unless they are maxed out in which case they hurt your score.
Suppose you have several credit cards, your total balance is $5000 and your credit lines total $10,000. With the car loan, you were using $20,000 of your $25,000 of available credit. By paying off the loan, your available credit goes down to $10,000 (lowers your score); your usage of that credit goes from 80% to 50% of your available credit (good) and you have a few months of on-time payments (good).
But the score is just one way lenders evaluate you. The next time you apply for a loan, you aren't carrying this loan, which will help your debt/income ratio, which is not part of the score calculation but is a big factor in qualifying for a new loan.