The amendment bans information about the deaths of Russian forces “during special operations” in peacetime.
The Kremlin has consistently denied sending regular troops and armour to help rebels in eastern Ukraine.
But a new report from the US says Russia has been using training camps near the border as “launching points of Russia’s war in Ukraine”.
The study by the Atlantic Council, published on Thursday, claims to have tracked Russian involvement in the conflict using photographs, videos and satellite images posted online.
President Putin’s move to ban information about peacetime military deaths comes amid fears of a fresh offensive by Russian-backed separatists.
Men wearing military uniforms ride atop a troop transporter during exercises at Kuzminsky military training ground in the Rostov region.
Reuters reporters said they had observed this week Russia’s army massing troops and weaponry – including mobile rocket launchers, tanks and artillery – at a makeshift base in Kuzminsky, near the border with Ukraine.
The news agency said many of the vehicles had number plates and identifying marks removed, while servicemen had taken insignia off their fatigues – similar to some unidentified forces seen in eastern Ukraine.
A ceasefire agreement was signed in Minsk in February, but heavy fighting has continued in some areas since then.
Before the amendment was signed by Mr Putin on Wednesday, the loss of troops was a state secret only in wartime.
The decree gives no details of what is meant by “special operations”.
For months there have been reports of secret burials of Russian soldiers killed in Ukraine.
Earlier this month, Russian blogger Ruslan Leviyev said he had found three graves of Russian officers killed by shelling in eastern Ukraine on 5 May.
Meanwhile the authors of the Atlantic Council report – including British weapons analyst Eliot Higgins – say satellite images have confirmed the movement of Russian troops and camp build-ups along the Ukrainian border.