If your insurance is AAA, State Farm or All State, your premium probably won't go. But it depends on your insurance company and also the state you live in.
When I got rear ended in bumper to bumper traffic in CA, my ML320 with tow hitch receiver shows no damage but the damage on the other party was very visible. The other party was also uninsured. I had to call CHP since wife had minor whiplash. When home, I called my insurance(Ameriprise through Costco) just in case wife's whiplash got worsened. Ended up we never filed any claim after all, but when the time came for renewal, my insurance bumped up more than 30%. That was only incident we ever reported!
Called to ask for explanation, were told it's just company-wide rate increase not the accident we reported. Shopping around for lower rates, we found out that accident had bigger role for the rate increase. So, your insurance may tell you they won't raise rate for this claim, there's some chance depending on your insurance company.
When we were insured with AAA for decades, they never hiked my insurance for not-at-fault accident, but their rate went up so high year after year for the first class service, we had to move to cheaper insurance.