Goikoetxea, 28, was one of the most wanted men in Spain.
Speaking at a news conference on Tuesday, Rubalcaba said: "We can't say this is the only Eta cell, but it was the most active, the most daring and the most wanted."
He said Goikoetxea's group was thought to have killed civil guard officer Juan Manuel Pinuel-Villalon in a May 14 barracks bombing and staged most of Eta's major attacks since the Basque group called off a unilateral ceasefire last June.
"The time between an Eta member exploding a bomb and being locked up is getting less and less," Rubalcaba said.
Rodolfo Ares, a leader of the Basque Socialist Party, said: "This is a special morning because today we feel a little bit more free, because several terrorists have been arrested."
The operation was supervised by Baltasar Garzon, a judge known for handling Spain's highest-profile Eta and civil rights cases.
Most of the arrests took place in Bilbao and the nearby towns of Elorrio and Getxo.
One member of the cell was captured in Malaga, southern Spain, and another in Pontevedra, Galicia, to the northwest.
The investigation of the group remains open, Rubalcaba said.
Tuesday's operation follows the explosion of four small bombs in Cantabrian holiday resorts in northern Spain on Sunday.
The attacks caused no injuries and marked the beginning of Eta's traditional summer bombing campaign against Spanish tourist areas.
|Spain's prime minister said Eta's only option is a unilateral surrender [AFP]
Eta, which is seeking an independent Basque state, declared a ceasefire in March 2006, raising hopes for an end to the group's four-decade campaign that has left more than 800 people dead in shootings and bombings.
However, Jose Luis Rodriguez Zapatero, Spain's prime minister, broke off peace talks after the group killed two people in an attack on Madrid airport in December 2006.
Eta officially ended its ceasefire in June last year.
Zapatero has ruled out further peace talks and says the group's only option is a unilateral surrender.
Spanish police have arrested 306 people accused of links to Eta since January 2007.
Francisco Javier Lopez Pena and three other suspected Eta chiefs were captured in Bordeaux in southern France on May 21.
"Not a single Eta member is going to be spared, all of them will face justice," said Rubalcaba.
Spain's Socialist government says the group, considered a terrorist organisation by the European Union and the United States, has been severely weakened by the number of high profile arrests.
Despite this, Eta has staged over a dozen attacks and two killings this year.