Snowden, who leaked details of sophisticated NSA electronic monitoring programs, left Hong Kong Sunday and traveled to Moscow before paperwork required to have him detained was completed.
U.S. officials said Sunday Hong Kong could have taken the whistle-blower into custody because the hold-up on paperwork was based on minor issues.
Feinstein, in an appearance on CBS' "Face the Nation," said she thought it was a "very big surprise" that China didn't arrest Snowden when it had the chance.
"I had actually thought that China would see this as an opportunity to improve relations, and extradite him to the United States," she said. "China clearly had a role in this, in my view. I don't think this was just Hong Kong without Chinese acquiescence."
Feinstein, the chair of the Senate Intelligence Committee, said the committee is more concerned about enabling "people to see the process that's followed" in surveillance.
"I think from the point of view of our committee, something that concerns me more is that we get an understanding in this nation that what this is all about is the nation's security," she said.