Hauschka, 27, strained his calf muscle during the Seahawks' victory over the Redskins on Sunday. He had made 24 of his 27 field goal attempts in the regular season and made all three of his attempts against Washington last week.
Clemons, who had 11.5 sacks this season, suffered a torn ACL and meniscus in his left knee in Sunday's win over Washington.
The Seahawks will face the Falcons in Atlanta on Sunday for the right to advance to the NFC Championship Game.
Longwell, 38, made 22 of 28 field goal tries for the Vikings last season but until Wednesday hadn't signed with a team since being cut in May after Minnesota drafted kicker Blair Walsh in this past April's draft.
Chukwurah has not played in an NFL game since 2007 with Tampa Bay. He spent the 2009 and 2010 seasons in the UFL with the Florida Tuskers, where he led the league in sacks.
Longwell and Seahawks general manager John Schneider were with the Green Bay Packers together until Longwell signed with Minnesota for the 2006 season.
His 94.4 field goal percentage over the 2009 and 2010 seasons -- 43 of 46 -- was the best in the NFL. Including nine years with the Packers, Longwell is 13th in NFL history with 1,687 points and fourth on the active list.
His career-long 55-yard field goal came on Oct. 14, 2007, to beat the Chicago Bears with no time left.
Information from ESPN.com NFC West blogger Mike Sando and The Associated Press was used in this report.