Bristol's Southmead Hospital announced on Thursday pest controllers would "remove" the animals in a "last resort" to ensure the "safety of babies".
The proposal was met with objections and sparked a petition which attracted hundreds of signatures.
The hospital said it had halted its plan and was consulting animal groups.
The hospital revealed last week that it had enlisted the services of a pest control company to capture and "humanely" deal with a group of foxes outside its maternity unit.
A post on Facebook said the animals were "potentially disease carriers" and with many of the unit's windows open over the summer there was a "potential risk of foxes entering the building".
But within hours, people demanded to know if any animals had been "killed or harmed".
Nikki Hamilton posted: "I love the NHS and will always defend to the hilt but not happy that exterminators are killing the foxes", while Caroline Littlewood said she was "appalled" by the plans.
The hospital has since posted it had halted its plans and it had not killed any foxes.
It said: "Foxes have lived peacefully on the site for a number of years. However, recently we have had more sightings of foxes particularly around our maternity unit.
"To clarify, we contacted pest control because we are particularly concerned about one of the foxes who looks like it may be unwell. The fox has become bolder in behaviour and is being sighted more regularly in public areas.
"So far we have contacted some alternative animal welfare organisations and we are pausing all existing activity while we consider their recommendations."
A hospital has "paused" its plans to remove foxes from outside a maternity unit which bosses believed posed a "risk" to newborns.