McCullum was hit by Australia fast bowler Mitchell Johnson high on his left forearm and received treatment on the area, which immediately swelled up.
He slipped on a protective arm guard and continued batting, eventually being dismissed for 50 in New Zealand's tense one-wicket victory over their trans-Tasman rivals.
"He looks a bit like Popeye," Hesson told reporters in Auckland on Sunday. "Other than that he's pretty good. It is pretty swollen, so we'll try and get that down first and make another assessment in a day or so."
Hesson said the New Zealand captain had not had an X-ray but he had been told it may have burst a burst blood vessel.
"All the signs are he'll be fine."
Hesson said he, like many of the 40,000 at Eden Park and more watching on television, had been battling inner turmoil in the final moments of the game after Mitchell Starc had bowled his side to the brink of victory.
Starc took career-best figures of 6-28 and had last batsman Trent Boult facing a hat-trick in the 23rd over as New Zealand chased 152 for victory.
Bolt saw out the over and Kane Williamson then belted a six off Pat Cummins on the first delivery of the 24th to clinch the one-wicket win.
"There was quite a bit going on underneath," Hesson said.
"Obviously Mitchell Starc had started swinging the ball nicely. Four guys were knocked over first ball they faced from him. He's a challenging guy.
"Trent showed a heck of a lot of character to leave a wide one when he had a fair bit of adrenalin going. It showed he was still thinking clearly.
"Kane realised he had to make a move, and to play the shot he did showed what a quality player he is.
"Those guys will be better for that experience. I think everyone will, to be fair."
(Reporting by Greg Stutchbury in Wellington; Editing by Nick Mulvenney)
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