In a comment, you clarified that the card you made the transfer to is maxed out. That's almost certainly the issue.
When most consumers think about utilization, they immediately think in terms of averages - if I have 4 credit cards with $2,500 limits, I have a grand total of $10,000 in credit card limit - if the sum of my 4 balances is $2,500 then I have a 25% utilization.
While that math is solid, it's not the entire story - scoring models typically also include a factor of each card's utilization. So - if you have those same 4 cards, but that $2,500 balance is on one of them and the other three have $0, you're doing to be scored differently than someone who has the $2,500 balance spread across all 4 cards.
Given that, something like a balance transfer can alter your score because it changes each card's utilization, even if it does not change your total utilization. Even if you have a good total utilization, if you have one card that's maxed out, it'll have a negative impact on your score.
Ultimately, the good news is that utilization is memoryless, only your most recently-reported utilizations are used when calculating a score. So, if or when you pay off that balance and the percentages change, your score will instantly increase. Or, if you move the balance back to the first card, the score change would instantly reverse itself. Because of this, it's not really important to be concerned over credit score changes as a result of utilization unless you're preparing to take out a new loan or otherwise do something where your score is important. Of course, you should always pay down card balances rather than incur interest, but in terms of utilization's impact on your score, as long as you "work" the utilization to be ideal in the month before needing to use your score, you'll be fine.
All that said, it's also possible that something else happened - perhaps even something fraudulent - it's wise to keep an eye on your score on a site like creditkarma or another service that allows you to view your credit report and/or explains changes to you. You've said that you didn't open or close any accounts, but there can be other reasons why your score may change. For instance, some utilities or other service providers will do a hard pull before serving you (the vendor that fills the LP tank at my home does for instance). Or, an old and closed account may have aged off your report, which could have driven average age of credit or other factors down.