It was not clear who is behind the posters declaring Dzhokhar Tsarnaev "not guilty".
They show pictures of Tsarnaev and his mother Zubeidat, and include an appeal for online donations.
The Tsarnaev family are ethnic Chechens but have lived mostly outside Chechnya.
Residents of Grozny say the posters most likely came from someone trying to make money out of the Boston Marathon bombings.
Dzhokhar's elder brother Tamerlan -- a fellow suspect -- was killed during a clash with police three days after the April 15 bombings, which killed three people and wounded more than 200.
Reports say the Tsarnaevs lived for years in Kyrgyzstan - in Central Asia - and Dagestan, another Russian republic in the North Caucasus which borders Chechnya.
Pro-Tsarnaev leaflets have also appeared in Kyrgyz capital Bishkek, BBC cited Russia's Interfax news agency as saying.
Police are trying to find out who stuck them on the walls of underpasses in the city centre.
The posters in Grozny follow an earlier campaign there in support of the Tsarnaevs. The authorities removed the earlier ones, which appeared April 24.
The latest posters in Grozny say: "This is Dzhokhar Tsarnaev, a 19-year-old lad accused of a terrorist attack in Boston. But as many people now know, that is a groundless accusation, there is absolutely no evidence against him."
"Now he is in a serious condition, in a prison hospital, he needs medical and legal help. Dzhokhar's parents ask you for help, to collect money for their son, whom they cannot lose, as they have already lost the older son, cruelly, unjustly. We will be grateful for any help, in the name of the Almighty do not remain indifferent."
The message includes a number for the Russian online payment system, Qiwi Wallet, and the Tsarnaev family address in the social network, VKontakte, BBC said.