Paul, was in Amarillo, Texas, during his US road trip along the iconic Route 66 with girlfriend Nancy Shevell, when a male fan approached him with his four-month-old son Jude.
When the Beatles legend was introduced to the baby he took out his harmonica and played "Hey Jude," which he wrote in 1968.
Record store owner Don Dunavin told Britain's Daily Mirror newspaper: "I was holding Jude and Paul walked right in front of us. I took two steps forward and shook his hand."
"He went to Jude, grabbed his hand and started talking to him. After we told him his name he said, 'I've got something for him.'"
"Jude was smiling at him. I told my wife to get the camera out and he stopped. He said, 'Please, no pictures.' But then started playing some more."
Don's wife, Lori, added: "Now it doesn't matter if Jude gets teased. The man himself played the harmonica for him."
