Cooper has made six changes to the starting line-up from last week's defeat against the Crusaders in Christchurch.
McKenzie shifts to full-back, after playing at fly-half in the Chiefs' past three games, and his brother, Marty McKenzie, who returns from injury, will wear the number 10 jersey.
Experienced lock Michael Allardice returns to combine with captain Brodie Retallick.
The return of Allardice moves dynamic forward Tyler Ardron back into number eight with Taleni Seu providing cover on the bench in jersey number 19.
Mitchell Karpik the other change in the pack to start with Lachlan Boshier ruled out with injury. In the backline, Japanese international Ataata Moeakiola secures his first start of the season on the left wing ahead of Etene Nanai-Seturo who will make an impact off the bench in jersey 23.
Amongst the replacements, Tasman loosehead prop Ryan Coxon will be hoping to make his Super Rugby debut in front of a home crowd at FMG Stadium Waikato.
Waikato's Luke Jacobson joins Coxon to earn his place in the twenty three for the first time this season.
Cooper said: "We have had a testing couple of weeks and we know the Hurricanes will be a strong challenge. We are not afraid of the contest on Friday, we have come together as a team and will focus on sticking to our structures and working on delivering our game plan."
Chiefs: 15 Damian McKenzie, 14 Sean Wainui, 13 Tumua Manu, 12 Anton Lienert-Brown, 11 Ataata Moeakiola, 10 Marty McKenzie, 9 Brad Weber, 8 Tyler Ardron, 7 Mitchell Karpik, 6 Mitchell Brown, 5 Michael Allardice, 4 Brodie Retallick (c), 3 Nepo Laulala, 2 Nathan Harris, 1 Aidan Ross
Replacements: 16 Samisoni Taukei'aho, 17 Ryan Coxon, 18 Angus Ta'avao, 19 Taleni Seu, 20 Luke Jacobson, 21 Te Toiroa Tahuriorangi, 22 Alex Nankivell, 23 Etene Nanai-Seturo
Date: Friday, March 15
Venue: FMG Stadium, Hamilton
Kick-off: 19:35 local (06:35 GMT)
Referee: Mike Fraser
Assistant Referees: Brendon Pickerill, Nick Hogan
TMO: Shane McDermott