Mark Chapman has been brought in as batting cover for Taylor.
Taylor picked up a tear in his left hamstring while fielding on the final day of Central Stag's Plunket Shield victory over Wellington Firebirds in Napier last Sunday (March 14).
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Taking to Twitter, New Zealand Cricket (NZC) on Wednesday (March 17) announced that Auckland Aces batsman Mark Chapman has been brought in as batting cover for Taylor.
Black Caps coach Gary Stead said the injury was precautionary and was hopeful Taylor would be available for the second ODI, slated to be held at Hagley Oval on March 23.
"It's a shame for Ross to have this happen on the eve of a series. It's a small tear and we're hopeful after some rest and rehabilitation we can get him fit for the second game in Christchurch," Stead said in an official statement.
"It's an exciting time for Mark who's come in and performed well recently for the T20 side, so we have full confidence he can do the job if called upon," he added.
Taylor will join the Kiwi team in Dunedin later on Wednesday in order to have the treatment of his injury.
The three-match ODI series between New Zealand and Bangladesh will kick-start on Saturday (March 20).