Wickremanayake, 73, replaces Rajapakse himself, who defeated former premier Ranil Wickremesinghe for the presidency last week in a campaign in which he vowed to review a peace process with Tamil Tiger rebels.
Wickremanayake is known as a hardliner and has previously advocated a military solution to the Tamil Tiger separatist insurgency which has claimed more than 60,000 lives since 1972.
The stock market took the appointment as a harbinger that a ceasefire brokered by Norway and in place since February 2002 could fall apart, traders said.
"The market picked up slightly at the opening and then it began crashing," Elton Ebert of Ceylinco Securities said. "There is a lot of selling pressure."
Rajapakse and Wickremanayake, ardent nationalists for the Sinhalese majority, oppose a devolution of power to the ethnic Tamil rebels that is a cornerstone of the current peace process begun by Wickremesinghe.
The benchmark All Share Price index plunged 156 points, or nearly seven percent to 2,172.83 in the first four hours of trading. This followed a seven percent plunge on Friday when Rajapakse defeated pro-market Wickremesinghe.
The president's economic affairs advisor Nivad Cabraal said the markets were unkind to the new administration.
"There is no reason for the market to behave like this," Cabraal told AFP. "The fundamentals are very strong and people who buy at these prices are going to make a killing in the short term."
Photographers were invited to Rajapakse's official residence for a cabinet swearing in ceremony, but the plan was shelved and only the prime minister took his oath of office, a government spokesman said.
Officials said the cabinet was still being finalised amid jockeying by key politicians for plum jobs.
Wickremanayake was prime minister under Kumaratunga briefly from 2000 to 2001 and was interior minister in her last administration. He had also acted as defence minister in Kumaratunga's absence.
The Tamil Tigers have yet to react to Rajapakse's offer of peace talks, made soon after his swearing in on Saturday following a razor-thin win in Thursday's presidential election.
However their website reproduced pro-rebel newspaper editorials which said talks were not on the cards.
Uthayan newspaper, in an editorial posted on the Liberation Tigers of Tamil Eelam website, said the Sinhalese majority had all but voted for war by failing to elect Wickremesinghe.
"Through electing a head who refused to accept that a just and permanent solution to one of the peoples of this island is an absolute necessity, the Sinhala nation has exposed its innermost feelings," the Uthayan said.
"Majoritarian chauvinism has come shining through." - AFP
-Amal Jayasinghe: firstname.lastname@example.org