Odeh said 10 of the injuries were moderate to grave. Many of the soldiers were treated for panic.
"They say it is in response to the continued Israeli military attacks against their activists throughout the Gaza Strip and the West Bank," Odeh reported.
"There are daily incursions and detentions in the West Bank, so the groups consider it a legitimate response against a military target."
Qassam rocket attacks from Gaza are frequent, but rarely cause injuries.
The homemade rockets are inaccurate with many falling in open spaces or in the town of Sderot.
Most land harmlessly but since 2000, 12 people have been killed in the salvoes.
The number of wounded was the highest in a single rocket attack launched from the Gaza Strip.
Hamas took over the Gaza Strip during fighting against the Fatah faction of Mahmoud Abbas, the Palestinian president, three months ago.
The strike on the army base could boost calls in Israel for a large-scale ground operation in the Gaza Strip against fighters behind the rocket attacks.
|The rockets often land in Sderot's streets [AP]|
Eli Yishai, the Israeli industry and trade minister, told Israel's Army Radio: "I think that, long, long, long ago, years back, we should have responded with a mighty force.
"There will be no choice but to take action, ultimately.
"There will be discussions, the military will makes its proposals, and the government will decide."
Ehud Olmert, the Israeli prime minister, said last week that Israel would "without hesitation and without pity" launch counterstrikes against fighters who fired the homemade rockets.
After the rocket attacks, a missile fired by Israeli forces hit a home in Beit Lahiya, a Palestinian town in northern Gaza, locals said, wounding a woman and her daughter.
Two Palestinian children were also injured on Tuesday when Israeli forces raided the Jenin refugee camp in the West Bank, Israeli forces detained 16 Palestinians.
Last week, Olmert ordered the army to draw up plans to curb the rocket fire, but did not endorse water and power cuts on Gaza's beleaguered population.
Pressure on Olmert to respond to the regular rocket fire has mounted recently after a projectile landed near a day-care centre in Sderot a day after the start of the school year. There were no casualties.
Ehud Barak, the Israeli defence minister, was quoted as telling ministers that until Israel has completed development of a rocket interception system, "the only solution is deep ground operations in Gaza".
"The time may be approaching where it will necessary to launch a major ground operation to stop the rocket fire," he was quoted as saying in a speech to directors of Israel's main arms manufacturing firms.