Adams has a hamstring injury, while Richards is nursing an ankle injury, with both players withdrawn from the USMNT roster. No replacements have been named.
It will be a critical game for the U.S. squad after its 2-0 loss on the road against Canada on Sunday. Adams, whose club team is RB Leipzig in Germany, played 69 minutes in Sunday's game, while Richards, who plays for Hoffenheim in Germany, was on the field for 90 minutes-plus.
Canada leads the CONCACAF standings with 22 points, while the USMNT and Mexico have 18 points each. Honduras is last with three points. The U.S. earned a 4-1 victory at Honduras on Sept. 8.
With a win over Honduras and three points against Panama on March 27, the U.S. could clinch a spot at the World Cup pending the results of other matches. A defeat or draw in either home game would put the U.S. in danger of missing its second straight World Cup.
"Our focus right now is finishing off the window with a win," U.S. coach Gregg Berhalter said. "If we can do that, we'll be in good position, and then it's about going to the last window and getting results, and we're confident we have a team that can do that."
This cycle has been marginally better, but every match has been tense until late: The Americans have been tied at half-time eight times and trailed twice, taking a first-half lead only once.
They have been outscored 4-2 in the first half, going scoreless eight times, but have an 11-3 advantage in the second.
"We've created enough in the first half to score more goals," Berhalter said. "I think we've done a good job of wearing teams down in the first half with both possession and transition. So we're doing a decent job. I think the last thing is just finishing those attacks.
"I'm happy that the team shows enough poise and composure to come out in the second half and still play strong."
The top three teams in the eight-team CONCACAF group advance to the World Cup later this year at Qatar. The fourth-place team enters an intercontinental playoff with one last chance to advance.
Information from the Associated Press was used in this story.