South Africa-born Berg suffered the injury while playing against Nottinghamshire in Barbados.
The 35-year-old will be assessed in the next two weeks to decide whether he will need an operation.
"If there is an operation then you're looking at probably mid-season," said Benkenstein.
"I'm hoping it's only six weeks if he doesn't have to have an operation," he told BBC Radio Solent. "I never like operations and there's a chance he can get better without the operation."

Francois Hollande was taking part in a ceremony to mark 70 years since Allied troops liberated the last Nazi camps at the end of World War Two.
"The worst can always happen," Mr Hollande said at the site of Natzweiler-Struthof in Alsace.
"We prevent it by knowing."
Most of the 50,000 inmates were French resistance fighters, but they also included Jews and gypsies. By the time of its liberation, almost half the prisoners had died.
The Nazis built and tested one of their first gas chambers at the camp.
France has been grappling with rising attacks on both Jews and Muslims after deadly shootings by Islamist gunmen in January, sparking fresh debate about growing social tensions, says the BBC's Lucy Williamson in Paris.
Commemorations have also been held in northern Germany to mark the 70th anniversary of the liberation of the Bergen-Belsen concentration camp, where an estimated 70,000 people were killed, including the young Jewish diarist Anne Frank.
The president of the World Jewish Congress, Ronald Lauder, remembered the first shocking images to emerge from the camp.
"We saw the bulldozers pushing naked bodies into open pits," he said, according to AFP news agency.
He remembered "the walking skeletons, the unbelievable sadness and loss," at a ceremony attended by about 70 survivors.
Another emotional ceremony took place at the site of another camp - Jasenovac in Croatia - to mark the 70th anniversary of an escape attempt by about 600 inmates.
Only 80 or 90 inmates escaped, with the rest shot by guards.

Top-flight sides Birmingham City and Manchester City will meet at the national stadium on Saturday, 13 May.
The attendance is now set to surpass the 32,912 that saw Arsenal Ladies beat Chelsea 1-0 in the 2016 final.
Wembley staged the event for the first time in 2015 and is set to continue doing so for the foreseeable future.
Birmingham - who won the trophy at Ashton Gate in 2012, in front of fewer than 9,000 people - are in their second final, while Women's Champions League semi-finalists Manchester City are yet to win the competition.
The 2016 Women's Super League One champions beat Liverpool in this year's semi-finals, while Birmingham knocked out 2015 winners Chelsea on penalties.
Hampshire coach Dale Benkenstein says all-rounder Gareth Berg could be miss up to half of the upcoming season should he require knee surgery.
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France's president has warned that anti-Semitism and racism "are still here" on a visit to the only Nazi concentration camp on French soil.
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The Women's FA Cup Final is set for a new competition-record crowd at Wembley, with 34,500 tickets already sold eight days before the 2017 final.