Walcott is set to miss the rest of the season after he ruptured his cruciate ligament during his side’s 2-0 win over Tottenham in the FA Cup on Saturday.
The 24-year-old has been ruled out for at least six months which means there is no chance of him travelling to Brazil for the FIFA World Cup in June.
"I just wanted to express my disappointment to him. It is a blow for him personally of course, and for both Arsenal and England,” Hodgson told TheFA.com.
The forward has been influential for Arsenal this season and his five goals in 14 Premier League appearances have helped the Gunners to secure their current status as league leaders.
"We had quite a lengthy conversation and it is such a shame that we have lost a player of his calibre for the World Cup, he has been incredibly unfortunate and we wish him a speedy recovery.
"Having worked with him for two years as England manager I know the character he has, and I know he will come back even stronger from this setback."
Walcott, a shock omission from Fabio Capello’s 23-man squad for South Africa in 2010, was an unused squad member at the 2006 tournament and will be 29 before he has the chance to appear in another World Cup.