SHANGHAI—China is snapping up stakes in private companies at a record rate, as the trade war, economic slowdown and credit squeeze heap pressure on entrepreneurs.

The investments mark a reversal after decades in which state-owned enterprises have shrunk in importance, as reflected in measures such as their share of the workforce or asset ownership. Since China’s public-sector companies are typically less efficient or innovative than their private rivals, the shopping spree could lead to a fresh drag on growth.

Private...