WASHINGTON—President Donald Trump, already embroiled in a trade battle with China, plans to ratchet commercial tensions higher by barring many Chinese companies from investing in U.S. technology firms, and by blocking additional technology exports to Beijing, said people familiar with administration plans.

The twin initiatives, set to be announced by the end of the week, are designed to prevent Beijing from moving ahead with plans outlined in its “Made in China 2025” report to become a global leader in 10 broad areas of technology,...