The Red Devils chief has thrown his weight behind the Norwegian coach, who come under pressure recently following United's disappointing start to the season.
As the club announced their financial results, Woodward said: "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.
"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."
Woodward also pledged that the club will support financial assistance for lower-league clubs amid the coronavirus pandemic.
He said: "We recognise that not all football clubs are in as robust of a financial position and that the Premier League has a responsibility to support the wider English football pyramid.
"We will continue to push for this support, both through emergency assistance during the pandemic, and through longer-term reforms to ensure that the success of the Premier League is reinforced for the benefit of the national game as a whole."
The executive added that United feel that they will be in a good position beyond the pandemic.
Woodward remarked: "While the Covid-19 pandemic continues to cause significant disruption, we are optimistic that the recovery and normalisation phase is gradually coming into view.
"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."