However, Wood has been given a warning after his shin made contact with Williams' head as he tried to secure possession for Wales in the 28-25 win over the hosts at Twickenham.
A warning equates to a yellow card.
Three yellow cards in the tournament lead to a disciplinary hearing.
On Sunday, Wood apologised to Williams with a message on Twitter. Wood wrote: "Really relieved to hear you're back on your feet OK mate. Horrible to see you stretchered off because of me. Hope you have a speedy recovery."
Full-back Williams, 24, though, could pay a heavier price for the clash as he can only make a gradual return to play under head injury protocols.
These could see him ruled out of Wales' remaining pool matches against Fiji and Australia.
Williams's potential absence adds to Wales's injury problems with centre Scott Williams (leg) and winger Hallam Amos (shoulder) set to be ruled out of the tournament.
Wales play Fiji in Cardiff on Thursday, before England host Australia at Twickenham on Saturday.

Tory Zac Goldsmith pledged to deliver a Southern Overground and secure funds for Tramlink, Bakerloo Line and London Overground extensions.
Labour's Sadiq Khan said he would freeze fares and crack down on what he called a "culture of excess".
Rival candidates want to cut fares but said Conservative plans were "uncosted".
Unveiling his manifesto in Ilford, east London, Mr Goldsmith said he would deliver planned upgrades to the District, Circle, Metropolitan, Hammersmith & City, Northern and Jubilee lines, and would replace "sub-standard" suburban rail services with a Southern Overground.
He also spoke of securing funding for Crossrail 2 and extensions to the Sutton Tramlink, Bakerloo Line and London Overground to Barking Riverside, saying that delaying or cancelling these projects would risk 250,000 jobs and 270,000 homes.
He said: "And it's why Sadiq Khan's Â£1.9bn black hole in the transport budget would be such a dangerous experiment, bringing gridlock to our capital, fewer new homes and meaning council tax hikes for every family in Greater London."
Outlining his transport pledges in Brixton, south London, Mr Khan recalled riding on the number 44 bus with his siblings, when his father drove the bus.
"I'll be the bus driver's son who makes commuting more affordable", he said, adding: "I will wage war on waste, excess and inefficiency within TfL and crack down on the culture of excess."
He also promised a four-year fare freeze, a review of Transport for London (TfL) management, projects which "truly benefit Londoners" and more women on TfL's board. He said he would look at the amount spent on agency workers and consultants, currently said to be Â£383m a year.
Lib Dem mayoral candidate Caroline Pidgeon said Mr Goldsmith's manifesto was "an uncosted wish list".
"He makes no mention of any fare rises, and he appears to be relying on government to keep on funding London's transport network."
Green Party candidate Sian Berry has promised to lower costs for outer London, introduce flat fares by 2025, allow transfer between buses and trains without an extra cost and support walking and cycling.
England flanker Tom Wood is free to play against Australia after he was not cited for the incident which saw Wales full-back Liam Williams knocked unconscious on Saturday.
[NEXT_CONCEPT]
Conservative and Labour mayoral candidates have set out their transport manifestos, with a "war on waste" and Tube and train expansions promised.