The word hippophobia refers to a fear of horses (apparently hippos are "water horses") and the words zoophobia refers to a fear of animals in general, but I can't seem to find a word for a fear exclusively confined to hippopotamuses.
To clarify, I am not talking about the healthy fear that a normal person would have of a large two ton animal being in their close vicinity, but an irrational fear of such a creature even when the situation would not warrant it, i.e. a true phobia. For instance, some children will seem to go through phases where they will have a phobia of something, becoming hysterical on sight of said thing even when they are in a safe protective setting where there is nothing to worry about.
Best Answer
It would be a common sense to have a fear of hippos so a phobia of hippos would be very unlikely. Hippos are the number one human killers among the mammals and they are very aggressive animals. They are also the most dangerous animals in Africa (after mosquitoes).
There is a word hippophobia which means "fear of horses" as you mentioned. It is because the word hippo comes from Greek which means "horse" and hippopotamus literally means "river horse". Equinophobia is used for fear of horses also.
So, there is no established term for the fear of hippopotamuses but it would be a rare case of zoophobia.
From wikipedia's zoophobia article:
From the book "Anxiety Disorders in Adults A Clinical Guide" By Vladan Starcevic, MD, PhD:
Though, there is a phobia of wild animals: agrizoophobia. Most of the sources say that it is rarely diagnosed and it usually effects people in urban lifestyle. Zoos and films are common triggers.
A detailed explanation: