It is the second time the hooker has skippered the Lions during the tour, having led them to a win over the Chiefs.
Coach Warren Gatland made the decision after the Lions lost the opening Test against New Zealand 30-15 on Saturday.
The second Test against the All Blacks is on Saturday, 1 July.
"We are obviously hugely disappointed with the result but it is important to regroup," said Gatland.
"We know there are a lot of players motivated to go out and get a result for the whole group.
"A few players put their hands up for selection from the Chiefs game and played their way into the Test team so they know that there is another opportunity for them on Tuesday against the Super Rugby champions."
Wing George North and centre Jonathan Joseph will both start against the Hurricanes, while Jack Nowell is at full-back.
Lock George Kruis is on the bench having played the whole 80 minutes of the first Test against New Zealand.
The All Blacks have released Julian Savea, Jordie Barrett and Ngani Laumape back to the Hurricanes for the game, while Nehe Milner-Skudder also starts.
British and Irish Lions: Jack Nowell (England), Tommy Seymour (Scotland), Jonathan Joseph (England), Robbie Henshaw (Ireland), George North (Wales), Dan Biggar (Wales), Greig Laidlaw (Scotland), Joe Marler (England), Rory Best (Ireland, captain), Dan Cole (England), Iain Henderson (Ireland), Courtney Lawes (England), James Haskell (England), Justin Tipuric (Wales), CJ Stander (Ireland).
Replacements: Kristian Dacey (Wales), Alan Dell (Scotland), Tomas Francis (Wales), Cory Hill (Wales), George Kruis (England), Gareth Davies (Wales), Finn Russell (Scotland), Jared Payne (Ireland).
Hurricanes: Jordie Barrett, Nehe Milner-Skudder, Vince Aso, Ngani Laumape, Julian Savea, Otere Black, Te Toiroa-Tahuriorangi, Ben May, Ricky Ricitelli, Jeffrey To'omaga-Allen, Mark Abbott, Sam Lousi, Vaea Fifita, Callum Gibbins, Brad Shields (captain).
Replacements: Leni Apisai, Chris Eves, Mike Kainga, James Blackwell, Reed Prinsep, Kemara Hauiti-Parapara, Wes Goosen, Cory Jane.

Nasri, 29, was an unused substitute for Thursday's International Champions Cup win over Borussia Dortmund in China.
Defender Gael Clichy revealed on Wednesday that Guardiola had exiled some players from first-team training until they meet certain weight targets.
And the new City boss said of Nasri: "He arrived a little bit overweight."
The France international missed six months of last season with a thigh injury he suffered in training.
Guardiola, who arrived at the club at the start of July, said the player's fitness is "much better now" and added: "Last season, he was injured in the season. We want to avoid that. We want the players on the pitch to be fit.
"We want their weight to be in the right place where they can run 90 minutes like Fernandinho and [Aleksandar] Kolarov and the others. Hopefully in the next two weeks, he will be OK."
When asked if he was pleased with Nasri's progress, Guardiola said: "I cannot have any complaints about the team. It's the opposite.
"The fans can be so proud of these players. In every training session, they've tried and tried with the rhythm we play."
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Rory Best will captain the British and Irish Lions for his side's next game against the Hurricanes in Wellington on Tuesday.
[NEXT_CONCEPT]
Manchester City midfielder Samir Nasri has not yet played for the club during pre-season because of his weight, says manager Pep Guardiola.