The jet was shot down by a Russian-made missile over eastern Ukraine in 2014, killing all 298 on board.
The West and Ukraine say Russian-backed rebels were responsible but Russia accuses Ukrainian forces.
The families' claim is based on the violation of a passenger's right to life, News.com.au reported.
The claim is for 10 million Australian dollars ($7.2m; Â£4.9m) for each victim, and the lawsuit names both the Russian state and its president as respondents.
Jerry Skinner, a US-based aviation lawyer leading the case, told News.com.au it was difficult for the families to live with, knowing it was "a crime".
"The Russians don't have any facts for blaming Ukraine, We have facts, photographs, memorandums, tonnes of stuff."
Mr Skinner said they were waiting to hear from the ECHR whether the case had been accepted.
The Kremlin said it was unaware of the claim, the Interfax news agency reported, but a senator with Mr Putin's party is quoted in state media as saying it was "legally nonsensical and has no chance".
There are 33 next-of-kin named in the application, the Sydney Morning Herald reported - eight from Australia, one from New Zealand with the rest from Malaysia.
Sydney-based law firm LHD Lawyers is filing the case on behalf of their families.
Flight MH17 crashed at the height of the conflict between Ukrainian government troops and pro-Russian separatists.
A Dutch report last year concluded it was downed by a Russian-made Buk missile, but did not say who fired it.
Most of the victims were Dutch and a separate criminal investigation is still under way.

1 June 2016 Last updated at 00:03 BST
Teams of riders charge together, firing their riles in unison.
But now for the first time, women have been taking them on... and winning!
Sahar Zand travelled to Morocco to meet the girls of Fantasia.

The data was posted on a procurement website, revealing details such as health conditions and social care needs.
Gloucestershire County Council (GCC) said it had "done everything we can" to remove the online material.
The victims of the breach had been informed and an investigation is under way, the authority added.
The council uses online procurement portals to post notices when urgent residential or non-residential care was needed for people with physical disabilities, learning disabilities or mental health needs.
But staff had attached personal "pen pictures" of adults requiring such urgent help to notices available to the public on the supplyingthesouthwest.org.uk portal, dating from the start of 2017.
The council's chief executive Pete Bungard "sincerely apologised" for the error, and said staff had already been retrained while an internal investigation was carried out.
A spokeswoman for the authority said GCC had "worked with the procurement websites and search engines" and added she was "confident the council has done everything it can to remove the information".
Earlier this year, GCC launched an investigation after it unwittingly revealed details online of a Â£500m contract for a controversial incinerator project.

The 40-year-old sank five birdies, including two in the final three holes.
That put him behind only American duo Shawn Stefani and Tom Hoge, and Korean Seung-yul Noh.
Miguel Angel Carballo, Brian Gay, Colt Knost, Dustin Johnson and Steve Stricker matched Donaldson, with Retief Goosen among those a further shot back.
This is the final PGA Tour event before the US Open - the second major of the year - takes place at Oakmont next week.
We've launched a new BBC Sport newsletter ahead of the Euros and Olympics, bringing all the best stories, features and video right to your inbox. You can sign up here.

The Environment Department published its Island Development Plan setting out planning policy for the island.
It took three years to produce and includes proposals for increasing the amount of affordable housing and the regeneration of old vinery sites.
Environment Minister Deputy Yvonne Burford claimed the plan balances the improving the economy with environment.
If approved by the States, housing developers building five or more units would be required to make up to 30% available as affordable accommodation.
Before the draft Island Development Plan is adopted by the States it will be subject to independent review by two planning inspectors.
Families of victims of downed Malaysia Airlines flight MH17 are suing Russia and its President Vladimir Putin in the European Court of Human Rights.
[NEXT_CONCEPT]
For centuries the Berber men of North Africa have proved their worth in the high octane, dangerous sport of Fantasia.
[NEXT_CONCEPT]
A council has apologised to 14 vulnerable adults whose personal details were published online.
[NEXT_CONCEPT]
Welshman Jamie Donaldson shot a four-under-par 66 to sit one behind the leaders after the first round of the St Jude Classic at TPC Southwind.
[NEXT_CONCEPT]
Housing developers could be made to make 30% of a development affordable housing under new government plans.