The ad, posted by NHS Leicester, was shot as if it had been filmed on a mobile phone and shows the baby being delivered.
The push aims to highlight concerns about teenage pregnancy to under-18s.
The ad was pulled by YouTube less than 24-hours after it was posted. YouTube said the video had been removed due to "terms of use violation".
The posting of gratuitous violence and people getting hurt are among YouTube's conditions.
The viral is still available via the campaign's website, hey-babe.co.uk, where a docu-drama on the subject is also planned for June.
The NHS trust has said it shot the viral ad as the leafleting and posters it has previously used have failed to have an impact on its target audience.