Whether or not the window can be replaced by your insurance policy depends on how the window was broken and what type of car insurance coverage you have. A minimum coverage policy is not going to help much, but some add-on riders may work to provide coverage even then.
If the window was broken in an accident and you were at fault, it can be replaced by a claim against your collision insurance. The insurer will not accept a collision claim for only a broken window, but they will replace the window as part of a larger damage claim.
In most other circumstances, you will need to have comprehensive auto insurance for it to cover a broken window. With comprehensive coverage, the window could be broken by any cause, even a stone thrown up from the road, and the insurance will pay. Keep in mind that there will be a deductible on your policy, and you may find out that it is more financially sound to just pay for the replacement out of pocket. For example, if the deductible is $300 and replacing the window costs $375, it does not make much financial sense to use the insurance for a $75 claim.
A number of window replacement companies will handle filing the claim for you. Since they work in close conjunction with insurance companies, they are able to pass the information along directly after you sign off on the replacement. That can save you some time and information, and it greatly increases the likelihood that the claim will be accepted without any problems.