The Turin club play a home match among Europe's elite for the first time in three years having earned a good draw against defending champions Chelsea at Stamford Bridge last month.
Juve have not lost in their last 45 Serie A matches but their Ukrainian visitors have, somewhat incredibly, won their last 25 games in all competitions.
"It is an important test tomorrow [Tuesday] and we want to deal with everyone," said Chiellini.
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"We face a very strong team, too under-rated. They have good players who could fit into most European teams.
"We have a lot of respect for Shakhtar. We still believe we can win but it will take a great performance.
"But the round does not end tomorrow. We are not back in the Champions League to exit in the first round."
First-team coach Massimo Carrera respects the work Shakhtar manager Mircea Lucescu, who has experience with Inter Milan, Reggiana, Brescia and Pisa, has done.
"They are very technical and have a coach who knows Italian football," he said.
"There are so many Brazilians who are dangerous with their counter-attack and the know-how to play football.
"We will have to attack them as we know they have a strong defence, conceding only six goals in 10 games."
Shakhtar forward Marko Devic, who moved from Metalist Kharkiv in the summer, believes their brilliant winning streak will be severely tested.
"Our fans expect us to play well in Turin so we'll do our best to get a draw at least, as every point could be crucial in the Champions League," he told uefa.com.
"It's a great pleasure to win game after game but we'll be judged by the (Champions League) matches against Juventus and Chelsea. They are the most important ones for every Shakhtar player and this is the moment of truth."
Full-back Olexandr Kucher is also wary of the threat Juve pose at home.
"Let's not forget that it will be an away match against the Italian champions," he said.
"The most admirable thing about Juventus is their stability. They are unbeaten in Serie A for a very long time.
"However, I don't want it to seem like we are scared. We are ready to fight as we want a positive result."