The embassy had distributed a "demonstration alert" to US citizens in Russia recommending they avoid protests in Moscow, Saint Petersburg and other cities.
The authorities sometimes interfere with mobile communication networks to make it harder for protesters to communicate among themselves and share video footage online.
The EU had already condemned an attempt to assassinate Navalny and his arrest on his return to Russia after treatment, but Michel has now expressed "grave concerns" directly to Putin.
Navalny's allies are planning demonstrations on Saturday in dozens of Russian cities in support of the Kremlin critic.
The report alleges that the 17,691 square metre mansion sits on a property 39 times the size of Monaco and features a casino hall, along with a theatre and a hookah lounge complete with a pole-dancing stage.
The central bank, which reports interventions with a two-day lag, will publish the total settlement figure for Jan. 15 and Jan. 18 on Wednesday, as the US market was closed for Martin Luther King Jr. Day on Monday.
The 44-year-old returned to Russia on Sunday from Germany, where he received treatment after being poisoned with what experts say was the Novichok nerve agent.
We are deeply troubled by the arrest of Aleksei Navalny, and call for his immediate release and for his due process rights to be respected in line with the rule of law.
Navalny accused Putin of ordering the attack, a claim the Kremlin vehemently denies. Russian police have not opened an investigation citing a lack of evidence.
For around a decade, Navalny has been the symbol of Russia's protest movement, after rising to prominence as an anti-corruption blogger and leading anti-government street rallies.