"That his career, and his life, was cut short in his prime is incredibly unfair.
"I don't have a blood brother, but I am very proud to have called Phillip my brother. I am a better man for having known him.
"Vale Hugh Dog. I will miss you forever, but I will not forget.
"Happy birthday bro."
Also posting a birthday tribute on Twitter, Clarke wrote that it "has been the hardest few days of my life".
Clarke's leadership during such a tragic time for the cricket community has been widely praised, with Cricket Australia team doctor Peter Brukner and chief executive James Sutherland both thanking him in recent days.
"Michael Clarke is Pharlap. All bloody heart. That statement would've been tougher than any innings. Plenty of pain & love right there," Paralympic gold medallist Kurt Fearnley posted on Saturday, one of many moved by Clarke's words.
Clarke on Sunday also wrote of the support forthcoming for Sean Abbott, the allrounder who delivered the ball that struck Hughes on Tuesday.
"Not one single person blames him in any way for what has happened. He deserves our full support," he noted.
"He will absolutely have mine whenever he needs it, and I know that also goes for the entire Australian cricket community.
"Sean, when you feel like getting back on the horse mate, I promise you that I will be the first to strap on the pads and go stand up the end of the net to hit them back at you.
"It's exactly what Hugh Dog would want us both to do."
Australian team coach Darren Lehmann joined in Sunday's social media tributes.
"Happy 26 th birthday Bruz! RIP #408 63not out! Love ya mate.", tweeted Lehmann.
Test spinner Nathan Lyon wrote: "Happy 26th Birthday BRAZ! We miss u mate! #408 #63notout63*"
The first Test between Australia and India was delayed on Saturday to ensure players could attend Hughes' funeral in Macksville on Wednesday.
The game could be abandoned, or potentially start on Friday or Saturday.
-AAP