Police were called to the zoo after the man threatened his girlfriend and attacked a zoo security guard, police spokesman Sonny Jackson said.
Police said the man was acting irrationally and repeatedly refused to comply with officers' commands.
As the man attacked the officers and zoo security guards, officers attempted to use a Taser in "contact mode," the Denver Post reported.
In contact mode, the Taser is placed directly against the suspect's skin, causing pain in one area of the body without affecting the body's full electrical system, Jackson said.
After he was restrained, officers called paramedics to examine the man, citing his "unusual behavior and extraordinary strength."
While waiting for the paramedics, he started to convulse and stopped breathing, police said.
He was taken to Presbyterian/St. Luke's Hospital where he was pronounced dead, the Post said.
Police said drugs and drug paraphernalia were found on the suspect, identified as Alonzo Ashley, 29.