The Swiss insurance association (SVV) said the estimate was an initial reckoning that would likely go higher.
The damage was largely centred on eastern Switzerland, affecting buildings and commercial goods.
Around 2,000 people or businesses had filed claims as of Tuesday, the SVV said.
Suisse Grêle, the agricultural insurance co-op, estimated that damage to crops totalled about 2.5 million francs.
The co-op received 600 calls from people concerned about damage from the rainfall that started on Friday and ended on Sunday.
Despite extensive TV footage of fields under water, a spokeswoman from the union of Swiss farmers said the deluge would have little overall impact on Swiss agricultural production, the ATS news agency reported.
In the canton of Saint Gallen, the parliament freed up 500,000 francs of lottery revenue to aid property owners who suffered damage but were without insurance.
A cantonal road between Schmerikon and Bollingen remains closed to traffic until further notice, ATS reported.
In the canton of Schwyz, a section of the A-14 autoroute, which closed over the weekend between Goldau and Brunnen, is open to traffic again.
The Gotthard rail line will be reopened to passenger trains between Immensee and Arth-Goldau, in the canton of Schwyz, on Wednesday, ATS said.
The section was closed to rail traffic on Sunday due to rockslides, with buses pressed into service to maintain the link for passengers.
The rain caused numerous rivers and lakes to overflow their banks in northern, central and eastern Switzerland and led to at least one death.
The ASA insurance group, however, described the weather event as “average” in gravity.
In neighbouring Germany, Chancellor Angela Merkel pledged 100 million euros ($130 million) in flood aid on Tuesday while touring hard-hit southern areas of the country.
The same storm that hit parts of Switzerland struck several countries in Eastern and Central Europe, leading to the evacuation of 8,000 people in Prague, and claiming the lives if 11 people across the region.
In Hungary, a state of emergency was declared along some areas of the Danube River, where water continues to rise.