The result ensured the two teams shared the spoils in the series after the first Test in Chittagong also ended in a draw. Match officials called off play at 2:08 pm local time (0808 GMT) after overnight showers and continuous drizzle made the ground unplayable.
Bangladesh were 269-3 overnight in the second innings, leading New Zealand by 114 runs. Left-handed middle-order batsman Mominul Haque remained unbeaten on 126 alongside former captain Shakib Al Hasan on 32 not out. Several hundred fans left the stadium dejected as they had been hoping to see Mominul complete a double century.
Bangladesh were under pressure on the fourth day, trailing New Zealand by 155 runs in the first innings before Mominul and Tamim Iqbal wiped out the deficit and put Bangladesh in front, adding 157 runs for the third wicket. Mominul, who also made 181 runs in the first innings of the first Test and aggregated 376 runs in the series, was named both man of the match and of the series.
Bangladesh captain Mushfiqur Rahim praised the consistency of his side.
"If you talk about the whole series, it was our target to consistently play well throughout," Mushfiqur said after the match. "It was not easy for us. We played a Test match after nearly five-six months. We didn't get that many chances to play longer-version matches. It was a challenge for us.
"It is a good sign that some players played well under pressure. We tend to play one Test well followed by a bad performance in the next one. "It was nice to see that we have backed our performance in the first Test with a good showing in the second one."
New Zealand captain Brendon McCullum was frustrated at failing to win the series but hailed his side's batting.
"I think obviously we came here and we wanted to win this Test series and we were expected to do so as well," said McCullum. "But if we strip it right back I think that the cricket we've played through the series has been very good. "I think our batting's been outstanding; our bowling has stood up in tough conditions.
"And whilst we didn't get the results, I think the cricket we played has been really good and I think a drawn series is a fair reflection because I also think that Bangladesh played some excellent cricket in this series as well."
The two teams will now play three one-day internationals and a Twenty20 international. The first ODI will be held the Sher-e-Bangla on October 29.