Solskjaer has fared better in the Champions League, having taken United back to Europe's elite club competition last season, but a defeat away to Istanbul Basaksehir last week increased pressure on the United manager.
Speaking on the release of United's quarterly financial results, Woodward said that Solskjaer retains the full support of the Old Trafford hierarchy.
"On the pitch, while there is still hard work ahead to achieve greater consistency, we remain absolutely committed to the positive path we are on under Ole as the team continues to develop," he said in a statement to investors.
United's financial results were the first to exclusively include behind closed doors games at Old Trafford, with year-on-year matchday revenue falling by 92 per cent to £1.7m as a result.
Commerical revenues also fell by 26 per cent due to the lack of an overseas pre-season tour and the partial closure of the club's megastore, but broadcasting revenues rose by 45 per cent.
“While the COVID-19 pandemic continues to cause significant disruption, we are optimistic that the recovery and normalisation phase is gradually coming into view," Woodward said.
"The club’s resilience and our strong commercial business continue to provide a solid foundation and gives us confidence in our long-term outlook beyond the pandemic, both on and off the pitch.”
Woodward added: "We miss playing in front of our fans and we are working hard together with our governing bodies and relevant authorities to ensure that fans can safely return as soon as possible.”
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