The Jefferson Parish Sheriff's Office announced the arrests in a news release.
Two women, who weren't identified, were riding in a vehicle when they reportedly saw Ealy and Kapanui urinating in the parking lot of an apartment complex around 12:42 a.m. Sunday, authorities said.
One of the women told Ealy to stop. Authorities said Ealy turned around while exposing himself and began making lewd comments. Moments later, Kapanui allegedly exposed himself to the driver of the vehicle and made lewd comments, the sheriff's office said.
Both players were jailed on $4,250 bonds.
"We are aware of the situation," said team spokesman Greg Bensel. "Our security department is working with the Jefferson Parish Sheriff's Office on this matter. We will have no further comment."
Ealy, 6-foot-3, 207-pound receiver, and Kapanui, a 6-3, 270-pound tight end, were acquired this year as free agents. Kapanui, a native of Palolo, Hawaii, is in his first season with Saints after playing at West Texas A&M. Ealy, who is from Clarksville, Tenn., is a two-year pro who played at Houston and for the Tennessee Titans in 2007.
Authorities would not say whether Ealy and Kapanui have hired attorneys.