A small group of investors, including descendants of the company's founder, had actively opposed the deal.
"We are definitely against this because the financial risks are too great and the expected benefits are quite limited," said Kazuhisa Takeda, a former director of the drugmaker and a member of the founding family, ahead of the meeting.
"I think M&A is quite necessary for Takeda's future but Shire is not the answer."
Chief Executive Christophe Weber has promised to turn the deal profitable by slashing costs. It predicts annual savings of at least $1.4 billion three years after completion, and expects to boost underlying earnings significantly from the first full year after closing.
Takeda also has a plan to sell up to $10 billion worth of non-core assets to pay back debt. Andy Plump, Takeda's global head of R&D, told Reuters that it is necessary to accelerate deleveraging for keeping its credit rating at safe level.
"We have a plan for divestiture that gets us to a place in three to five years that our credit agencies are OK with. Our credit rating is likely to tick down a notch, but still above junk bond status, which is critical for us," he said in an interview.
Analysts have said it may be difficult to integrate the two companies.
Toshiba Corp's acquisition of Westinghouse over a decade ago and Japan Post Holdings Co's $4.9 billion bet on Toll Holdings are widely seen as examples of many Japanese companies having paid high valuations in cross-border deals only to face massive write-downs later.
But they also said Takeda has little choice but to seek growth abroad, with industry pressure to gain access to cutting-edge treatments amid declining revenue from older drugs that must compete with cheaper generics.
Even with the acquisition of Shire, some said Takeda will need to bolster its lineup of experimental therapies to compete in the longer term.
Shire's haemophilia business, for example, is already starting to face strong pressure from a competing drug being marketed by Roche as well as new gene therapies now in development.
"It's crucial whether the drugmaker can reinvest profits from the deal into seeds for developing future drugs," said Kazuaki Hashiguchi, a senior drugs analyst at Daiwa Securities.
"The benefits of the deal will last for a limited time, as no treatments can avoid patent expiration."