Serena had beaten Swede Rebecca Peterson in straight sets on Monday and was due to face sister Venus but the injury means her participation at the May 26-June 9 French Open is in doubt.
Zverev, who has not got past the quarter-finals at any tournament since reaching the Acapulco final in early March, did little to suggest he could be a contender at Roland Garros after a 7-5 7-5 defeat by home favourite Matteo Berrettini.
Roared on by a partisan home crowd at the Foro Italico, Berrettini took the opening three games before the German, 2017 champion and last year's runner-up, regained his composure.
Berrettini then saved five break points to take a 6-5 lead before the rattled Zverev, who beat the Italian in the same round last year, threw away the opening set with two unforced errors and a double fault.
They traded breaks early in the second before Zverev, who saved a match point in the 10th game, committed another flurry of errors, capped by a forehand into the net that handed Berrettini a memorable win.
"The environment was great, the match that I played was horrendous," said the 22-year-old Zverev.
KYRGIOS ANTICS
In first-round action, David Goffin produced two blistering sets to fight back and beat Stanislav Wawrinka 4-6 6-0 6-2 while Nick Kyrgios treated the crowd to an array of his antics in a 6-3 3-6 6-3 victory over Russian Daniil Medvedev.
The flamboyant and unpredictable Kyrgios again displayed his best and worst as he combined spectacular shots with an outburst of poor behaviour.
The Australian won the opening point of the match with what is fast becoming a trademark underarm serve and breezed through the first set before cheers from the crowd turned to jeers amid a second-set meltdown.
Having dropped serve to hand Medvedev a 5-3 lead, Kyrgios blasted a ball over the stands, then bent over and turned his backside to Medvedev and finally exchanged words with the umpire before the Russian held to force a third set.
As if nothing had happened, Kyrgios got back to business as he hammered in aces and winners, having also capped some good forays to the net with confident volleys to book a second-round clash with Norwegian Casper Ruud.
Goffin dropped the opening set before he blew Wawrinka away in the next two, the decisive moment coming in the second game of the third when the Belgian saved a double break point at 1-0 down.
He won the next five games and, although the Swiss briefly delayed the inevitable, Goffin was able to celebrate after his frustrated opponent blazed a forehand into the crowd.
Victoria Azarenka of Belarus knocked out holder Elina Svitolina 4-6 6-1 7-5 as she dug deep in a second-round evening match that was twice interrupted by rain in the second set.
Ukrainian fifth seed Svitolina appeared to be cruising in the third set as she served for the match at 5-2 up but the resilient Azarenka rallied to claim the last five games.
Ashleigh Barty had to work hard for a 4-6 6-3 6-4 win over Viktoria Kuzmova to reach the third round, while Kristina Mladenovic cruised past French compatriot Caroline Garcia 6-1 6-2 in their first round clash.
The leading men get their campaigns underway on Wednesday when world number one Novak Djokovic, fresh from winning last week's Madrid Open, takes on Canadian Denis Shapovalov.
Holder Rafael Nadal faces Frenchman Jeremy Chardy, while Roger Federer meets Portugal's Joao Sousa.
(Writing by Zoran Milosavljevic; Editing by Toby Davis and Ken Ferris)
