The cuts represent roughly 5-6 percent of Sinopec's average daily output target for this year at 4.5 million bpd.
"The run level will be reduced quite deeply for this month. Almost every plant is taking some cuts, because demand, especially of diesel, is weak," said one Sinopec refinery source.
"The diesel stocks are brimming," said a second refinery official.
Chinese refiners normally set their monthly production targets the previous month, but they sometimes make last-minute adjustments based on domestic supply and demand situations.
The sources did not provide a total throughput rate for June, or a level of May operations, but one said on average Sinopec processes 18-19 million tonnes of crude a month.
Diesel sales in some areas posted negative year-on-year growth in April and May, a Sinopec fuel marketing official told Reuters last week, as demand from industries slowed.
Implied oil demand in China, the world's second-largest fuel market, inched up 0.4 percent in May year-on-year, and rose marginally from April, when the figure fell for the first time in more than three years.