Paul, who gained notoriety on social media and has a popular video blog or "vlog" on YouTube, filmed the video in Aokigahara, which is known as "the Japanese Suicide Forest" because of its reputation.
According to media reports, the video showing a man who had hanged himself, received six million views before being removed amid a firestorm of outrage on Twitter.
Adding to the anger were outtakes of the video -- which remained in circulation on Twitter -- in which Paul is seen laughing and joking about the incident.
"When my brother found my sister's body, he screamed with horror & confusion & grief & tried to save her," actress Anna Akana tweeted.
"You do not walk into a suicide forest with a camera and claim mental health awareness."
Another Twitter user wrote, "i'm truly sickened by this logan paul situation. i lost my brother to suicide... my brother took his own life by hanging himself... how insensitive and sick can you be to film someone in that state."
In his apology, Paul said he had posted the video in a mistaken effort to draw attention to the problem of depression and suicide.
"It's easy to get caught up in the moment without fully weighing the possible ramifications," he said in the statement.
"I'm often reminded of how big a reach I truly have & with great power comes great responsibility... for the first time in my life I'm regretful to say I handled that power incorrectly. It won't happen again."
"Our hearts go out to the family of the person featured in the video," a Google statement said.
The statement added that YouTube prohibits "violent or gory content posted in a shocking, sensational or disrespectful manner" and that such content is allowed only "when supported by appropriate educational or documentary information."