Lawmaker Michael Ellis admitted he was being "mischievous" when he posed the question to Ms May at a select committee hearing.
Prince William's wife Catherine is due to give birth to Britain's future monarch at the private Lindo Wing of St Mary's Hospital any day now.
"Until relatively recently there was a convention that home secretaries attended royal births, I understand this happened with her majesty the queen," he said. "Do you have any plans to visit the Lindo Wing any time soon, following this convention?"
Ms May countered that the centuries-old custom no longer existed.
"It is no longer the case that the HS is required to attend a royal birth, but I suspect Mr Ellis with your royal connections you might have more information about these things than I do," she said.
Asked why the convention ever existed, she explained: "It goes back many centuries... The home secretary had to be there to evidence that it was genuinely a royal birth and that a baby hadn't been smuggled in."