The BBC Question of Sport star shared a series of heartbreaking images charting his child's recovery with his more than 250,000 Twitter followers on Wednesday.
Dawson, 43, said that he and his wife, Carolin Hauskeller, had been debating whether or not to post the "upsetting" pictures of young Sami:
Been umming and ahhhing about whether I should write the next post but my wife and I have agreed it's important. The pic may be upsetting!!— Matt Dawson (@matt9dawson) February 17, 2016
The slideshow first shows Sami in his hospital bed, covered in spots and fitted to a collection of tubes.
But, as he appears to gradually get better, the pictures show the toddler posing with his father and receiving a cuddle from his older brother, Alex.
Dawson added the hashtag #vaccinateNOW, adding his support to growing calls for all children to be given a meningitis vaccine.
Almost 250,000 people have signed a petition calling for all children to be given a meningitis vaccine following the death of a two-year-old girl.
The 2 weeks of hell we've just had cos of Meningitis. Sami lucky due to amazing people @GreatOrmondSt ??#vaccinateNOW pic.twitter.com/JMJ4X2h8r2— Matt Dawson (@matt9dawson) February 17, 2016
Faye Burdett, from Maidstone, Kent, died on Valentine's Day after fighting the infection for 11 days. Her story, told by her mother Jenny, has been widely shared on social media including Facebook and Twitter.
Faye's family said they are enduring "a pain you cannot describe" after the toddler contracted meningitis B.
Since September last year, a vaccine to protect against meningitis B has been available on the NHS for babies aged two months, followed by a second dose at four months and a booster at 12 months.
Manufacturer GlaxoSmithKline (GSK) hopes to have increased stocks in the UK by the summer. The NHS programme is unaffected.
