Along the way, the prime minister will stop in Kuala Lumpur, Harper's first visit to Malaysia since taking office in January 2006.
It's all part of a continuing Conservative government push into Southeast Asia that got off to a slow start and has since been hobbled by mixed messages.
The week-long trip to Malaysia and Indonesia, the prime minister said in a release, will "further Canada's interests, advance regional trade liberalization and promote Canada as a business partner of choice."
However, some experts say Canada is playing catch-up at a time when the emerging Asian tigers face economic turbulence of their own.
This week, the Canadian Imperial Bank of Commerce released figures that show foreign investment in Canada has plummeted more than 90 per cent so far in 2013 compared to last year, down to $2 billion from $27 billion.
Mergers and acquisitions have also felt the squeeze, down to $8 billion this year compared to $66 billion in the same time frame in 2012.
"Not everyone is getting the message that Canada remains open to the world," CIBC executive Jim Prentice, Harper's former industry minister, told a business audience in London earlier this week.
"In fact, some are coming to believe the opposite."
So it's no surprise that International Trade Minister Ed Fast is firing up his frequent flyer points, stopping first in Bali this week — where Harper will later attend the Asia Pacific Economic Co-operation summit — and then hitting Singapore and China.
It will be Fast's second trip to China this year, and his 13th trip to Asia overall since being appointed trade minister in May 2011. Finance Minister Jim Flaherty is not attending the APEC summit in Bali, although Foreign Affairs Minister John Baird will be on hand.
Yuen Pau Woo, the president of the Asia Pacific Foundation of Canada, said Canada has "been playing catch-up for a long time" in Southeast Asia, dating back to before the Conservatives came to power.
Jean Chretien, in 1996, was the last prime minister to visit Malaysia, and Harper took almost four years after coming to office before visiting China — a delay that was undiplomatically noted by Harper's host when he arrived in Beijing in December 2009.
Woo said that since 2008, the Harper Conservatives have had "a lot of enthusiasm" for Asian trade and investment, but results have been mixed.
"I would say that the easy part of the Canadian effort to build stronger ties with Asia is coming to an end. Now we're entering the hard part," Woo said in an interview from Vancouver.
"This is where I would be very keen to see some concrete measures to address long-term engagement."
Harper will be using his Malaysia and Bali visits to talk up the Trans-Pacific Partnership, a fledgling trade pact among 12 Pacific Rim countries that is still being negotiated. Indonesia, the APEC host, and China — the economic giant of the Pacific — are notably absent from the TPP.
Harper will no doubt also be asked about Canadian foreign investment rules that have clamped down on spending by state-owned enterprises.
Prentice, the CIBC executive, noted this week that Chinese investment has "essentially stopped" in Canada since huge takeovers in Alberta's oilpatch by the China National Offshore Oil Corporation and Malaysia's state-owned Petronas were grudgingly approved last year — and the rules subsequently changed.
Woo said the CNOOC and Petronas decisions and other legislative changes in Bill C-60, last spring's budget implementation bill, have made foreign investors leery.
"The easy part is to say, yes, we want investment from Asia. Everybody says that," said the Asia-Pacific Foundation president.
"The hard part is making it easy for them to invest. Instead we are doing the opposite. So what's going on here?"
Perhaps it was no coincidence that Harper's trade minister was out beating the drum Thursday on a major investment in Mississauga, Ont., by a subsidiary of Swiss biotech company Roche Holding AG.
"Foreign investment is linked to one in 10 Canadian jobs, making it a key driver of the Canadian economy," Fast said in a release.
"Attracting new foreign investment supports jobs and prosperity for Canadian workers and their families."
Note to readers: This is a corrected story. An earlier version had Yuen Pau Woo's name misspelled.
Also on HuffPost