The Liberal party councillor said the new centres would be developed over the next two years by his Speranza Foundation, a charity helping young people, the long-term unemployed and disabled people to reintegrate into the job market.
With childcare currently costing about 100 francs ($106) a day, rising to a daily rate of up to 140 francs ($150) in some places, paying for childcare is not an option for everyone in Switzerland.
In order to give more of the population access to childcare, Ineichen wants to eventually create a network of hundreds of low-cost nurseries that will be "affordable for people with a normal income", newspaper Le Matin reports.
According to Ineichen, Switzerland suffers from an acute shortage of qualified workers.
"It is therefore very important that mothers who want to work can return to the labour market," he said in a statement.
Ineichen wants to set a price of around 70 francs ($75) a day for low-cost daycare centres for children aged between four months and nine years.
The children will be divided into mixed-age groups of 10 to 12 in centres that will offer childcare services from two to five days per week, depending on the parents' needs. The centres will remain open from six in the morning until seven in the evening.
The first low-cost childcare centre is scheduled to open in Beromünster, canton Luzern, in April.