Smith was arrested at 2:10 a.m. by the Washington State Patrol and released from a King County correctional facility on his personal recognizance -- meaning in lieu of posting bail -- at 9:27 a.m., records show. No other information was immediately available.
"Geno is fully cooperative with the investigation," Smith's attorney Jon Fox said in a statement. "I hope that an open mind can be kept by all as the facts are ascertained."
In a tweet, Smith wrote that "being arrested brings a taint onto the reputation that is impossible to undo, no matter what really happened. I'm asking all of you to hold back on judging me the same as you would do for a friend or family member. I'll have more to say down the road & ask that you bare with me."
The Seahawks returned to Seattle on Sunday evening after closing out their season with a 38-30 win over the Cardinals in Glendale, Arizona.
Seattle coach Pete Carroll said Smith took part in end-of-season meetings Monday after he was released from custody.
"I checked in with him. We have to let his people handle all that," Carroll said. "He was in the [team] meeting today with us. I don't have anything other than that to give to you on that."
Smith, 31, served as Russell Wilson's backup the past three seasons and stepped in during the three-plus games in October that Wilson missed with a broken finger. He completed 65 of 95 passes for 702 yards, five touchdowns and one interception. The interception ended the Seahawks' comeback bid against the Los Angeles Rams in Week 5, when Smith took over for an injured Wilson in the second half.
The Seahawks went 1-2 in his three starts.
Smith is scheduled to be an unrestricted free agent after playing on a one-year, $1.2 million contract in 2021.
The Associated Press contributed to this report.