Factories in the Shanghai area are slowly returning to production in a closed-loop system but supply chain disruption is expected to continue for some time.
Companies were last week asked to submit plans to stop of the spread of Covid-19 before they could re-start production.
In total, 666 companies have been white listed by authorities to restart production, mainly in the automobile, semiconductor and energy sectors.
Electric car manufacturer Tesla is one company reported to have restarted production at its factory with workers required to sleep onsite in order to meet the closed-loop requirements.
However, the re-start of production is not without its issues, the South China Morning Post reports, with difficulties getting workers to sites and disruption to the supply of parts causing issues.
In its latest update, freight forwarder Flexport reported continuing supply chain issues.
"The central government is also assisting companies in key industries resume production with the goal of stabilising China’s supply chains during virus outbreaks," the company said.
"This will take some time to implement as a shortage of raw materials also presents a challenge in resuming production and trucking capacity is still limited.
"Flight capacity continues to be greatly reduced during this period and ad-hoc cancellation is expected if demand is low.
"Market rates maintain at relatively high levels due to the ongoing supply chain disruptions."
Flexport added: "Nearby cities such as Suzhou, Wuxi, Kunshan, etc. are still in partial or full lockdown with very limited trucking capacity available."
Rate portal Freightos added that the Shanghai shutdown could result in pent-up demand, while it added that cargo was building up in other locations.
"This lull in volumes and rates is expected to be followed by a surge in pent up demand and volumes – and possibly rates as well – once Shanghai reopens.
"And while congestion at destination ports like LA/Long Beach has improved somewhat, it is still a major problem.
"Air cargo diversions away from Shanghai are clogging up area airports. And despite a significant decrease in available exports, the cancellation of an estimated 40% of air cargo capacity out of Shanghai is helping to keep air rates elevated.
"Freightos Air Index China - North Europe rates have increased 40% since the start of the lockdowns to $8.69/kg last week."
The latest figures from Accenture's Seabury consulting show that airfreight capacity out of Shanghai is currently down by around 40% compared with the level recorded in March.
Freighter capacity is down by around 12,000 tonnes per week and bellyhold capacity has been reduced by around 4,000 tonnes per week.
Shanghai went into strict lockdown at the end of March as the city tried to contain an outbreak of the Omicron variant.
Authorities are hoping to ease lockdown measures this week if there are no new cases reported outside of the quarantine and isolation system.
However, outbreaks are now being reported in other cities in China such as Xian and Suining.
