"That the economic opening will translate into a political opening is inevitable," Foreign Minister Jose Manuel Garcia-Margallo told the conservative daily newspaper ABC.
"Another thing is the speed at which this will take place, and this is something that depends fundamentally on the regime," he added.
Cuba approved a foreign investment law a year ago, dangling steep tax cuts and investment security in the hope of luring badly needed capital.
Business interest in Cuba has boomed since December, when the United States and Cuba announced a historic rapprochement, ending five decades of enmity between the Cold War foes.
"There will be more information, more people will go to Cuba, more tourists. And they will go out more, they will travel. As a result, they will get to know other realities and that will favour a political opening," the minister said.
The number of Cubans travelling abroad surged by 23.7 percent last year to 355,000, according to official statistics published earlier this month.
Cuba eased travel restrictions in 2013, allowing Cubans to legally visit other countries, after being strictly controlled following the Cuban revolution.
Garcia-Margallo said there needs to be "national reconciliation, fundamentally in Cuba and also with Cubans in the diaspora" as well as an amnesty for dissidents.
"And then there should be democratic elections where everyone is accommodated," he added.
Four centuries of Spanish colonial rule ended in Cuba in 1898 with the Spanish-American War, although Spaniards continued to predominate among the island's wealthy landowners until the 1959 revolution.
Spain is Cuba's third-largest trading partner and its largest European investor, according to Spain's foreign ministry.