Animal Rebellion said the red dye represents the blood on the 'government's hands'.
Protesters from the organisation were in the square, with one of them stood knee deep in the fountain holding a placard.
The protester was approached by Metropolitan Police, before being escorted away.
Tweeting about the stunt, Animal Rebellion posted a series of videos which showed one of the group walking around the fountain while pouring red dye in to the water.
Animal Rebellion tweeted: "Animal Rebellion have now dyed the Trafalgar Square fountains red, symbolising the blood that is on the hands of the UK Government.
"We are here today to demand that the government prevent future pandemics by ending animal farming and transitioning to a plant-based food system.
"This crisis could have been prevented. The science tells us that 3 out of every 4 new infectious diseases originate from animals.
"The UK Government must protect the people, not support climate-destructive and exploitative industries."
The protest was announced on Friday (10 July), with the event being dubbed 'Blood On Your Hands'.
The event's official Facebook page read: "We are at a turning point in human history.
"It's becoming clearer every day that the Government isn't capable of getting us out of the coronavirus mess, or preventing climate breakdown and animal suffering. They are more concerned with getting us back to 'normal' as rapidly as possible.
"But it's normal that is killing us."
It continued: "So as the UK lockdown begins to ease, we stand at the crossroads:
"A plant-based food system OR a broken food system. We have a choice.
"Bail out people and the planet OR bail out the industries that are killing us. We have a choice.
"Trust the people OR trust a negligent government. We have a choice.
"Mass extinction OR mass action. We have a choice. We are at a turning point in human history."
The Met Police confirmed on social media that officers attended the planned protest.
Two people have been arrested on suspicion of criminal damage.