Since November, Chinese-backed Canyon Bridge Capital Partners has been seeking approval for a $1.3bn (£984m) deal to buy Lattice Semiconductor.
Canyon Bridge said it was "disappointed" by the decision.
The order comes as the US has been toughening its stance on China's intellectual property practices.
In its announcement, the Trump administration said it was concerned about the "potential transfer" of intellectual property from Lattice. It also cited the use of Lattice products by the US government.
Mr Trump's order was in line with an earlier recommendation by the US committee that reviews foreign transactions.
That step typically decides such matters, but the companies made the rare move to appeal directly to the president in an effort to win approval.
Lattice, a chipmaker that makes about 70% of its revenue in Asia, has said it did not think the deal posed a security risk.
In an emailed statement, Canyon Bridge did not address the security concerns raised by the US government.
The company, which is backed by the China Venture Capital Fund, said it would continue to pursue other investments.
"We are obviously disappointed in today's decision by the President of the United States to forgo what we believe to be an excellent deal for Lattice's shareholders and its employees by expanding the opportunity to keep jobs in America," the company said.
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