The arrest came on Tuesday, a day which saw police intensify their search in the capital city of Stockholm.
He was arrested in a restaurant outside Rasunda which is the name of Sweden's national soccer stadium located in a suburb just north of Stockholm.
Earlier in the day police had issued an arrest warrant for a suspect.
"We have indicted a man in absentia. He is suspected of the murder on reasonable grounds," Stockholm police spokeswoman Agneta Styrwoldt-Alfheim told Reuters.
An indictment in absentia means police have named a suspect but no arrest has been made.
Lindh, 46, died on Thursday from stab wounds inflicted by an attacker in an upmarket Stockholm department store a day earlier.
"We have indicted a man in absentia. He is suspected of the murder on reasonable grounds"
One of Europe's most respected and best-liked diplomats, Lindh had served as foreign minister since 1998 and was tipped as a possible successor to Prime Minister Georan Persson.
The murder shocked Sweden just days before a landmark referendum on whether the country should adopt the euro single currency was defeated despite Lindh's strong stand for a 'yes' vote.
Sweden has enlisted the help of foreign police services, and has compiled a classified profile containing "very sensitive material" of the suspected killer, Wessling said.
While detectives would not rule out that Lindh's killer may have escaped abroad, possibly to neighbouring Finland, this lead was "not more interesting than any other", she said, a view shared by Finnish investigators.
Police said that several people had been questioned in connection with the Lindh case, but all of them had been released.