Vegas Golden Knights president of hockey operations George McPhee said the forward was taking supplements not approved by the team and without its knowledge.
"Needless to say we're extremely disappointed with the result, but we are very supportive of the program," McPhee said. "Unfortunately, Zykov knowingly took supplements, tested positive and is suspended, and we support the suspension."
Zykov is eligible to return against the Arizona Coyotes at T-Mobile Arena on Nov. 29.
McPhee said he learned about the positive test Wednesday after having conversations with Zykov and his agent.
"We were completely in the dark until that point," he said. "We seemed to be the last to know."
Zykov has two assists and seven shots on goal in seven games this season. The Golden Knights claimed him on waivers from the Edmonton Oilers on Dec. 29, 2018.
"I want to apologize to my family, my teammates, and the Golden Knights organization and fans," Zykov said in a statement. "I will work hard during my suspension to ensure that I put myself in the best possible position to contribute to my team when my suspension is over."
Zykov is the second player from the Golden Knights to be suspended for violating the terms of the program. Defenseman Nate Schmidt was suspended for the first 20 games of last season.
Schmidt was vigorous in his denials about using a banned substance, and the Golden Knights backed him in public statements.
McPhee said the suspensions to Schmidt and Zykov were distinct in their own ways and not reflective of any team issue.
"I think it's a fair question," he said. "We have certainly the same result in terms of the suspension, but completely different circumstances.
"In one instance we had a player ... had a substance that entered his body, it was a testable amount. We were convinced by all the evidence that we had that it was accidental or involuntary. And the second, a player knowingly took substances without our consent or recommendation, and he tested positive.
"We're supportive of our players, but they're completely different circumstances. One we defended vigorously, the other it's pretty black and white."
Under the terms of the NHL/NHLPA Collective Bargaining Agreement, the suspension of Zykov is accompanied by mandatory referral to the NHL/NHLPA Program for Substance Abuse and Behavioral Health for evaluation and possible treatment.
Zykov was selected by the Los Angeles Kings in the second round (No. 37) in the 2013 NHL Draft. He has 15 points (six goals, nine assists) in 47 NHL games with the Carolina Hurricanes, Oilers and Golden Knights.
NHL.com independent correspondent Danny Webster contributed to this report