Hi there and thanks for your question.
Although visine is not recommended for dogs, putting one drop in his eye will not harm him.
There are several different types of visine and some of them contain a product that is a vasoconstrictor (something to make blood vessels smaller). In people it is possible for this vasoconstrictor to contribute to them getting glaucoma which is very serious. We haven't seen the same thing happen in dogs.
However, the vasoconstrictor in the visine can cause some temporary relief but if it continues to be used can lead to something called "rebound hyperemia" which means that the blood vessels that were made small respond by getting even larger.
If your dog has a red eye, there has to be a medical reason for it. It is possible that he has simply bumped his eye on something and has some bruising. However, most red eyes are usually a sign of infection. Usually we will see some discharge with infection too. If there is suspicion of infection it is important to have your vet examine the eye to make sure there is no obvious scratch on the cornea which is a very serious matter.
One other possible reason for a red eye is glaucoma which is very serious as well.
If your dog seems fine and is not squinting or has no discharge from the eye you are probably ok to wait for 24-48 hours to see if the redness goes away. Otherwise he should see the vet soon!
I hope all is well!
I hope this information helps! I will be online for a short while more. So, if you have more concerns about this question you can just hit reply. However, my baby will be waking up from her nap soon and I will be offline after that. If that happens I will respond when I come online again. Or, if my answer has been sufficient, please hit accept. Thanks!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.