A photo released by Bush's office shows two-year-old Patrick, who is undergoing leukemia treatment, and the elderly ex-president sporting bald heads and similar blue polo shirts and khakis.
A smiling Bush sits in his wheelchair, now his primary mode of mobility, and Patrick sits on his lap.
The 41st president took the no-hair plunge after noticing that members of his security detail, known as the Bush Protective Division (BPD), had done the same.
Bush and his wife, Barbara Bush, lost their second child, Robin, to leukemia 59 years ago when she was four.
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The couple have contributed to a fund set up to help with Patrick's bills.
Apart from his lack of locks, the former president has made a fashion splash in recent months as his penchant for colorful socks has gained traction in the media.
Bush dressed his feet in a superman motif for his 89th birthday in June and put on a bright-pink pair for the unveiling of his son George W. Bush's presidential library in Texas in April.
Last week Bush was honored for his "Points of Light" volunteer program by US President Barack Obama.
Bush, who served as president from 1989 to 1993, is the oldest living former US president, part of an elite club that includes his son, Jimmy Carter and Bill Clinton.