Nothing has been heard from Mr Yasuda, 42, since he disappeared after entering northern Syria in July last year.
In the video he appears to say Japan's government has ignored his plight.
Japanese media say a Syrian man in Turkey told them he posted the video and that Mr Yasuda was being held by the jihadist group al-Nusra Front.
The group, al-Qaeda's affiliate in Syria, has killed foreign hostages before, but also released some in return for a ransom or as part of a prisoner exchange.
Al-Nusra is violently opposed to so-called Islamic State (IS), which killed two Japanese hostages last year, contractor Haruna Yukawa and freelance journalist Kenji Goto.
In the one-minute video posted online on Wednesday, the man says in English: "Hello, I am Jumpei Yasuda and today is my birthday, 16 March."
"I love you, my wife, father, mother, brother. I always think about you. I want to hug you. I want to talk with you. But I can't any more."
"I have to say to something to my country. When you're sitting wherever you are, in a dark room, suffering with the pain. There's still no one. No one answering. No one responding. You're invisible."
After watching the video Japan's foreign minister said the government was doing all it could, but it had not received a ransom demand.
"I just want him to come back safely," Kyodo news agency reported Yasuda's mother telling reporters.
"We don't know anything and can't do anything. We can do nothing but wait," she said.
An acquaintance of Yasuda, Hitoshi Takase, said he was worried about the missing freelance journalist.
"From the image and the voice, I think it is him without doubt. He looks worn out and exhausted."
The Japanese government was criticised for not doing more to save Haruna Yukawa and Kenji Goto, who were beheaded by IS militants in January 2015.
The Japanese government says it believes a video posted on Facebook is of Japanese journalist Jumpei Yasuda who is missing in Syria.