Zverev's comeback delayed by new injury, could be out for months
Zverev has not played since June after undergoing surgery to fix damaged ankle ligaments following an injury he suffered during his French Open semi-final against Rafa Nadal.
The world number five had been included in Germany's squad for the group matches but was later replaced by Yannick Hanfmann.
"I am very disappointed to miss out on playing this week," Zverev told the Davis Cup website on Monday. "It was a massive goal for me to play here because it is my hometown ... but there is nothing I can do about it.
"I have a bone edema issue which causes me quite a lot of pain. I don't know if it happened yesterday or not but yesterday in practice with Oscar (Otte) it got to the point where I couldn't run or walk anymore.
"I subsequently found out that it was a bone edema, which means I won't be able to participate here and it is not a question of days, it is more a question of weeks or most likely even months."
Zverev reached a career-high ranking of world number two in June.