Will Homeowners Insurance Cover Injury? 
That is going to depend on who is injured and the cause of the injury along with the policy inclusions and exclusions possibly less your deductible . If you are asking about someone being injured on your property that your are deemed responsible for then your homeowners liability coverage may provide for this . Remember every policy is different . Please read your policy completely to understand the coverage provided and any exclusions that there may be or contact your local agent to have them go over the policy with you . 