A downpour led the umpires to suspend and then call off play after an early tea break with the game evenly poised.
New Zealand had dismissed the hosts for 282 early in the morning thanks to Neil Wagner's maiden five-wicket haul, but Bangladesh struck back through Shakib.
He took two wickets in his first two overs, with New Zealand in trouble at 32-2 at lunch before Kane Williamson and Ross Taylor rebuilt.
Rubel took a stunning catch at deep square leg as the New Zealand captain fell for 11.
Resuming on 228-5 at start of play, Bangladesh managed to add only 54 more runs in the face of tight bowling.
Wagner finished with 5-64, making full use of overcast conditions to induce some edges from the batsmen, after play resumed 30 minutes early to make up for overs lost on the opening day due to rain.
"So I'm pleased with that," he said.
"Every opportunity you get, you want to put your hand up and make the most of it," said Wagner, who replaced left-arm spinner Bruce Martin for this Test.
"For me personally it was tough to miss out on the first Test, but it's one of those things; that's the nature of the game."
"When you get another chance you've got to use it and you've got to grab it with both hands.
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