The 29-year-old, who became a Wimbledon champion for the second time after beating Milos Raonic in the final on Sunday 10 July, talked about sleep.
In the clip above the Duke of Cambridge can be heard saying to Murray: “Congratulations, I don’t know how you manage it with no sleep.
“How is your daughter doing, alright? Is the family good?”
Murray replied: “Yeah, she’s great, yeah, she’s actually sleeping!
“The last three nights she slept through, the first three months were tough but she’s five months now.”
The Duke of Cambridge replied: “Good omens.”
Murray’s wife, Kim Sears, gave birth to the couple’s first child together - Sophia Olivia - in February 2016.
Over the past five months, critics have suggested that becoming a dad has caused Murray’s performance to dip.
She said he “generally looked exhausted” and the “pressure of raising a child” was showing on court, according to the Daily Star.
However Murray hit back, telling The Mirror: “I would rather be getting up in the middle of the night and helping Sophia than winning every tennis match and her thinking when she grows up, ‘Actually, you know what, he was a s****y dad but he won a lot of tennis matches, so well done.”