Yes, this should be covered under your collision coverage.

Collision CoverageCovers damage to your car when your car hits, or is hit by, another vehicle, or other object. Pays to fix your vehicle less the deductible you choose. Coverage is limited to the terms and conditions contained in the policy.

Read more about your coverage on our Auto Insurance Coverage Definition page.

Comment Update: Typically, one claim should not cause your insurance costs to increase. Most companies have a claim threshold that must be paid by them before raising your rate. Minor damages usually fall below the threshold, unless it is high value vehicle that costs a lot to fix minor damages. If it is one of many claims or violations then you can expect your rate to increase.