SHANGHAI—The threat of skyrocketing prices for vegetables and other essentials has prompted authorities in China to impose fines and monitor supermarkets to keep costs down amid a coronavirus outbreak that has people hunkering down across the country.

In one extreme example, the price of lettuce surged to nearly eight times the usual price and the cost of Chinese cabbage jumped to around five times the usual price at one Carrefour supermarket in Shanghai, the city’s Market Supervision Administration said on its website Monday....