The Spaniard aggravated the problem during the ATP Finals, where he lost to Jannik Sinner in Sunday's title clash, with his withdrawal dealing another big blow to organisers the International Tennis Federation.
"I'm so sorry to announce that I won't be able to play for Spain in the Davis Cup in Bologna," Alcaraz said on Instagram on Tuesday.
"I have edema in my right hamstring and the medical recommendation is not to compete.
"I've always said that playing for Spain is the greatest thing there is, and I was really looking forward to helping us fight for the Davis Cup. I'm going home heartbroken."
Sinner, ranked No.2 in the world, pulled out of the tournament last month before defending champions Italy confirmed his absence.
Italy, who have won the past two Davis Cups, will also be without Lorenzo Musetti, who withdrew citing physical and family reasons.
Musetti's place is expected to be taken by Lorenzo Sonego who has been in Turin practising in recent days.
Italy will face Austria on Wednesday while Spain play the Czech Republic on Thursday in the quarter-finals with the final on Sunday.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Alexander Smith and Ed Osmond)
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