Oh, that sounds just terrible, because urine is somehow irritative and may give rise to some slight problems with us, especially babies. Anyway, you should try to get some mild normal saline to wash its eyes and get some anti-biotic eye drops to deal with the effects. That is not serious if treatment is provided. Try to be careful in the future.
Because the baby's eyes are sensitive, you should not use the eye drops. Although it has the role to clear the eyes, it has great stimulates on the baby's eyes. You could just use the clean cloth with some warm water to rub the eyes. You could also make baby laugh and blink more which could also let the urine in the eyes get disappear soon. You could have a try.
This is normal for a baby. Just wash him clean, and he will be fine. The urine which gets in his eyes won't do any harm to him, as most of the urine is water. If he is suffering from red eyes, you can first wash away the urine with water. Most likely, he doesn't need any special care just because of urine getting in eyes, as this is very common and harmless for babies. Just remember, next time you change his diaper, cover his front first.