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The 30-year-old left-hander, capped once by England in Bangladesh in March 2010, was diagnosed with blood clots on the lung in November, preventing him travelling to Australia with the second-string England Performance squad.
Carberry was sidelined with the problem until last month, with his whole career in the balance.
But in only his third Championship match of the season he helped First Division strugglers Hampshire stage a remarkable rally at the Rose Bowl.
Hampshire were 59 for two at one stage but Carberry, who struck two sixes and 43 fours, was brilliantly supported in a massive third-wicket stand of 523 by South Africa's Neil McKenzie, who made 237.
Their partnership was the ninth-highest in all first-class cricket and the second highest for the third wicket behind the 624 shared by Sri Lanka stalwarts Kumar Sangakkara and Mahela Jayawardene in a test match against South Africa at Colombo in 2006.
Sangakkara and Jayawardene's stand is also the highest for any first-class wicket.
But Carberry and McKenzie's partnership easily topped the previous third-wicket County Championship best of 438 unbroken made by Graeme Hick and Tom Moody for Worcestershire against Hampshire at Southampton in 1997.
Replying to Yorkshire's imposing first innings 532 all out, Carberry's triple century, which lasted more than six hours and spanned 427 balls – effectively 71 overs – saw him guide Hampshire to 599 for three declared on Friday's final day of four.
There was still time for Yorkshire to make 40 without loss in their second innings before the match, unsurprisingly, ended in a draw.
The largest partnership for any wicket in Championship history was the 555 put on by Yorkshire openers Percy Holmes and Herbert Sutcliffe against Essex at Leyton, east London, in 1932.
