The journalist, Salud Hernandez-Mora of Spanish newspaper El Mundo, went missing in northeast Colombia over the weekend.
The Spanish foreign ministry and her newspaper said on Monday she appeared to have been kidnapped by the National Liberation Army (ELN), the second-largest guerrilla group fighting in Colombia's half-century conflict.
"I have told the security forces, our generals, commanders and the chief of police to deploy all forces necessary to find her and free her if she is being held," Santos said.
No group had yet claimed the suspected kidnapping, he said.
El Mundo said Hernandez-Mora, a prominent journalist and long-time correspondent in the South American country, was last seen on Saturday in the Catatumbo region.
She "has been detained by guerrillas," the daily said online, citing Colombian military sources.
"The difficult-to-access area is controlled by the ELN," it added.
Speaking in Brussels, Spanish Foreign Minister José Manuel García-Margallo said the government also believed Hernandez-Mora had been taken by the ELN.
Starting as a peasant uprising in the 1960s and drawing in various armed groups and gangs, the conflict in Colombia has killed more than 260,000 people, uprooted 6.6 million people and left a further 45,000 missing.
The government is closing in on a deal with the country's biggest guerrilla group, the Revolutionary Armed Forces of Colombia (FARC).
It recently announced it would enter formal peace negotiations with the ELN. But the issue of ransom kidnappings - long the guerrillas' main source of funding - is already threatening to derail the talks.
The government accuses the ELN of kidnapping at least seven people so far this year.
Hernandez-Mora, who also works for the Colombian daily El Tiempo, was last seen Saturday in the town of El Tarra, according to a statement Sunday by Colombia's defense ministry.
El Mundo quoted a nun from the town as saying she saw the journalist covering a local demonstration over the disappearance of two children, who have since been found.
Santos has staked his presidency on ending his country's bloody conflict, considered the last major armed confrontation in the Western Hemisphere.
Inspired by the Cuban revolution, the ELN was founded in 1964, the same year the FARC launched its uprising.
Officials estimate the ELN currently has some 1,500 members and the FARC about 7,000.