The £14million signing flew home to the Central American country at the weekend, after what are thought to be the remains of his 16-year-old brother Edwin were discovered 150 miles from the capital Tegucigalpa.
Edwin, the youngest of five football-playing brothers, was seized by armed kidnappers from his home in the coastal town of La Ceiba following Wilson's move to Birmingham in August 2007. He moved to Wigan in January 2008.
Palacios had left the Spurs team hotel in Liverpool yesterday morning ahead of the club's 0-0 draw at Everton.
A Spurs spokesman said: "Wilson has gone home, obviously, on compassionate leave.
We would not expect to see him again for a while."
Spurs have just two games left this season, at home to Manchester City next Saturday and then away to Liverpool on the season's final day, May 24.
The club are in mourning now for the second time in a matter of weeks following the murder of a relative of one of their players.
Earlier this month striker Jermain Defoe's half-brother Jade, 26, was attacked in an east London street.
Club manager Harry Redknapp said: "It is quite amazing and tragic that two of our players have suffered the loss of a relative like this within a couple of weeks of each other."
Palacios heard news from his family at around 1.00am on Saturday morning while he was at the team hotel, Malmaison, in Liverpool.
And he sat in the hotel lobby until 7am before calling Redknapp in his hotel room with the news.
Redknapp said: "The lad had heard from his family at one in the morning what had happened, and his brothers, I believe, have identified the body.
"He sat around the hotel lobby with his case packed until 7am because he didn't want to wake me.
"I'm amazed with him. But we organised for him to be driven back to London so he could get a flight home."
Redknapp said: "You couldn't wish for a more calm and likeable lad, football is not really that important after this."
Palacios, 24, who signed for from Wigan in January, has also been singled out for praise by former boss Steve Bruce for his dedication during such personal turmoil.
Redknapp added: "He is a wonderful lad and if his brother was anything like him, he's one of the most respectful people I have come across, he is unbelievable.
"Wilson's mother has been in London to see him on her first visit to England. And she only left on Friday.
"She would have been flying back home and would not know about the tragedy until she got home."