A mother went to drop off her children at Ryders Green Primary School in Claypit Lane when a woman approached the car, opened the back door and tried to unclip the baby from its seat.
The would-be abductor fled in a white van when she was confronted by the mother.
Police have been informed but so far nobody has been arrested. The suspect was not known to the mother.
Parents have been urged to report anything suspicious and a nearby school has issued a warning to pupils and parents.
Staff from Hanbury Primary School, which is a 10 minute walk away in Hanbury Road, warned children over 'stranger danger' as a result of the incident.
Lucy Blackmore, headteacher from Ryders Green Primary School, said: “We were made aware of an incident that occurred off school premises on Monday morning.
“This was reported to the police.
“We’ve have reminded parents and children about the importance of staying safe.”
A spokesman for West Midlands Police said: "Police are investigating reports that a woman tried to take a four-week-old baby girl from a baby seat in West Bromwich on Monday.
"The woman tried to unclip the belt in Claypit Lane, Hill Top, at around 9am but was stopped by the child’s mother.
"She is then believed to have made off in a white van. The baby was unhurt and enquiries are under way.
"We understand that this would have been a very shocking incident for the child’s mother so we are asking for anyone with information to contact us via live chat at west-midlands.police.uk between 8am to midnight, call 101 anytime quoting 20SW/212584Z/18 or contact Crimestoppers anonymously on 0800 555 111."