There is no problem doing this unless you are on an enterprise account. Distribution certificates expire anyway, so eventually it will happen that you need a new one. Go ahead and delete away.
You can also find this question asked, answered, and asked again many times over on the Apple Dev forums (e.g. here’s one), so google around there if you’re still hesitant.
About Enterprise Developer accounts:
With thanks to Mike’s comment
An App store app gets resigned with an Apple certificate when it goes on the store. Revoking the cert in the provisioning portal therefore won’t affect it. Enterprise apps use the original certificate, which means revoking it will cause the app to stop functioning on all devices it is installed on. If you revoke an enterprise account’s certificate, all apps installed on all employee devices will stop working