New Zealand Cricket communications adviser Callum Elder told Hawke's Bay Today last night the nature of the players' illness was viral.
"We're told it's more of a viral thing as opposed to anything else."
A source also told Hawke's Bay Today it was Ross Taylor's birthday on Sunday and a bucket of fried chicken was bought in celebration. The chicken was eaten by some, but not all, of the players.
Meanwhile, fast bowler Adam Milne is the only player with a minor niggle. He damaged the AC joint in his shoulder taking a catch at the end of Afghanistan's innings on Sunday, but Hesson was confident he would be fit for selection for Friday's game.
Hesson maintained there would be no risks taken with players against Bangladesh.
"If guys have a niggle we won't force it with the gaps between games.
"When you've got two games in 21 days (between the Australian group game on February 28 and the quarter-final on March 21) we're not going to make it one in 21 in terms of preparation," he said.
"If these guys are fit and still performing they'll get first chance."
New Zealand have stuck with the same XI for all four group games, and are unbeaten, to top their group.
"We are in the middle of a World Cup and it's not a matter of thinking about tomorrow; it's a matter of making sure we do not drop the ball and keep putting in good performances."
During its time in Hawke's Bay, the team stayed at the Crown Hotel in Ahuriri.
The hotel's management would not discuss its guests.