The incident, which took place in Manila's upscale financial district of Makati, is the latest embarrassment for the country's police force.
Makati police chief Senior Superintendent Froilan Bonifacio expressed outrage and said the accused policemen may have carried out similar extortion scams in the past.
"I'm not just shocked. I'm angry, for God's sake. Maybe they have been doing this thing for years," Bonifacio told news agency AFP.
The five policemen approached the German tourist at a Makati shopping mall on January 29 and initially accused him of buying counterfeit goods. When he denied this, they accused him of illegal drug possession, Bonifacio said.
When this failed to scare him, the policemen threatened to arrest the German for supporting "terrorism". To prove his innocence, the policemen said he must buy laptops for their station, said the police chief.
The policemen took the German man to a luxurious mall where he was forced to buy six laptop computers with his credit card, according to Bonifacio.
After the purchase, the policemen set the tourist free but warned him not to tell anyone of the incident.
However, a German embassy spokesman said the tourist reported the matter to consular officials, who informed Makati police commanders.
The suspect policemen have had their weapons taken away and could be sacked as well as being hit with criminal charges, Bonifacio said.
The German embassy gave no other details about the case, but praised police commanders for taking action against the five.
"The embassy is very satisfied with the reaction of the national police command. It shows that they are determined to go after these people who abuse their position," embassy deputy head of mission Ralph Timmermann said.
Last month, a Manila policeman was sacked after a video was leaked showing him torturing a suspected criminal, while another was arrested after being accused of raping a street vendor inside a police station.
In the highest-profile incident to tarnish the image of Manila's law enforcers recently, an ex-policeman hijacked a busload of Hong Kong tourists last year in a bid to be cleared of graft charges. Eight of the tourists died as police bungled a rescue attempt.