One of the Sienna minivans covered by the third major Toyota recall this month.

Toyota will recall 694,000 older Sienna minvans due to a problem with the shift lever that could result in unexpected rollaways.

The problem involves Toyota Siennas produced at the maker’s plant in Indiana and sold from model-years 2004 to 2005 and from 2007 to 2009.  The vast majority of the vehicles – 615,000 in all – were sold in the United States. Another 56,000 went to Canada, with a small number also sold in Mexico, Germany and Guatemala.

The problem centers around the vehicle’s gearshift lever which, according to Toyota can experience damage to the shift lock solenoid. If that occurs, a driver can inadvertently nudge the lever out of the Park position without first depressing the brake.  In turn, that could allow the vehicle to roll away if it isn’t on a level surface.

The maker emphasizes that the Sienna van cannot shift out of Park on its own, however. The lever must be manually pushed.

(Toyota recalls more than 1 million hybrids and CUVs due to suspension defect. Click Here.)

Toyota acknowledges receiving reports of 21 “minor” accidents” in the U.S., with another three reported in Canada. Two of those resulted in bruises and other minor injuries.

The Toyota Sienna is the second-best-selling minivan in the American market, just behind the Dodge Caravan. But like many other minivans, its sales have been declining in recent years as family buyers opt for more stylish alternatives such as crossovers and SUVs.

Toyota is one of several makers that have experienced rollaway problems in just the last year.  The list also includes such brands as General Motors, Chrysler and Honda, the latter ordering a recall covering more than 800,000 vehicles last December. BMW, meanwhile, faced a class action suit alleging it dodged a recall for a similar problem. The case was tossed out by a California judge after a recall was finally ordered.

The Sienna campaign is just the latest in a series of recalls involving a variety of Toyota vehicles this month. In all, nearly 2 million vehicles sold in the U.S. alone have been involved.

Toyota has, in fact, had more vehicles involved in safety-related recalls than any other manufacturer during four of the last five years. It is on track to be at or near the top of the list again in 2013, vying for that dubious achievement against Honda which has also recalls several million vehicles this year for a variety of problems including faulty airbags that can inadvertently deploy. That led to the recall of 400,000 minivans and SUVs last month.

(Airbag problems force major Honda Recall. Click Herefor more.)

Japan’s second-largest automaker, Nissan, today recalled 900,000 vehicles due to potential stalling problems. Most of those vehicles were sold in Japan, but about 100,000 Infiniti M luxury sedans shipped to the U.S. were also covered.

(For more on the latest Nissan recall, Click Here.)