The Kasabian musician played opposite Williams at this year's Soccer Aid charity match at Old Trafford on Sunday (May 27).
Pizzorno suggested that the Take That singer should embark on a tour soon after his first baby is born.
"I told Robbie at Soccer Aid he should go on tour for the first three months after his daughter is born in September," he told The Sun.
"The first three months are horrific. Your life just becomes about getting covered in poo and talk about nappies."
Robbie Williams is expecting his first child with wife Ayda Field later this year.
Pizzorno was awarded the 'Man of the Match' award for his goal during Soccer Aid, which he dedicated to bandmate Tom Meighan, who also recently welcomed his first child.
Williams said last year that he plans to go on tour to support the release of his next studio album, which is expected to be released this year.