Inflation stood at half a percent in the year to June, down from 0.6% in May, according to the Federal Statistics Office.
Cheaper food and drinks offset a 15.4% jump in petroleum products linked to the war in the Middle East.
Rents remained the biggest driver of household costs, up 1.4%.
The strong Swiss franc is cushioning imported inflation — Switzerland's rate sits well below the eurozone's 2.8% and the US at 4.2%.
Economists say the Swiss National Bank is now unlikely to move interest rates in the coming months.
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