Philippine and German officials confirmed that 70-year-old Jurgen Kantner had been killed after being held for three months
by the Islamist militant group.
It was the second time Kantner, 70, had been abducted. He was held along with his partner, Sabine Merz, by Somali pirates for nearly two months in 2008.
Abu Sayyaf posted a gruesome video of its militants killing the man with a curved knife. The video was distributed by the SITE Intelligence Group.
"The Federal Chancellor condemns the abominable act, which once again shows how unscrupulous and inhumane these terrorists are. We all must stand together and fight against them," German Chancellor Angela Merkel's spokesman Steffen Seibert said.
Philippines President Duterte apologized to Germany on Tuesday for his troops "failure" to prevent the killing.
"I am very sorry that the hostage, a national of your country, has been beheaded. There's a massive operation going on. We really tried our best. We have failed. That has to be admitted," he said.
Philippine Secretary Jesus Dureza, the Presidential Peace Adviser, said the government strongly condemned "the barbaric beheading of yet another kidnap victim."
"Up to the last moment, many sectors, including the Armed Forces of the Philippines, exhausted all efforts to save his life. We all tried our best. But to no avail," he said in a text message to CNN.
The group had demanded 30 million Philippine pesos ($600,000) in exchange for Kantner's release, setting a deadline of February 26.
Abu Sayyaf announced in November last year that they had kidnapped Kantner and his partner in the waters off Malaysia's Sabah state, according to Philippine officials.
Merz was shot and killed by the militants soon after.
In September, Abu Sayyaf freed a Norwegian man it had held captive for almost a year, according to CNN Philippines.
War against Abu Sayyaf
The beheading emerges as the Philippine government wages a war against Abu Sayyaf, based in the restive Muslim-majority province of Mindanao in the country's far south.
Abu Sayyaf is a violent extremist group of some 200 to 400 members that is largely fragmented.
The Philippines is a predominantly Catholic country, but the south has historically had a large Muslim population. Abu Sayyaf's stated aim is to establish an independent Islamic state on the southern island of Mindanao.
The group first became active in the early 1990s and was responsible for bombings across the southern Philippines and in the Malaysian state of Sabah.
The seas around the Philippines are the most pirated in the world, according to data producer IHS Markit.