The viral shows grainy footage of a group of jeering teenagers as they watch a schoolmate deliver a blood-spattered baby in the middle of the playground.
YouTube removed the video on Monday, less than 24 hours after it had been posted online, for breaching its terms and conditions for violent and gratuitous content.
A YouTube spokesperson said: "YouTube has clear policies that prohibit inappropriate content on the site, including nudity, gratuitous violence, and hate speech.
"We also don't allow videos that aim to shock and disgust, unless there is a clear educational or documentary context."
The video site has not removed a second version that shows NHS Leicester branding and contact information at the end. The viral is available on the NHS website at Hey-babe.co.uk.
The campaign was created by London's The Rocket Science Group after the NHS trust decided previous leafleting and posters campaigns had failed to have an impact on its target audience.
A spokeswoman for NHS Leicester said the video had been viewed nearly 750,000 times online in the past three days, with queries for additional information coming from around the globe.