Atlanta-based rapper 21 Savage, a British citizen, is being held by US officials due to an expired visa.
His real name is Shayaa Bin Abraham-Joseph and he moved to America as a child.
A statement on Jay-Z's Facebook page says Savage "deserves to be reunited with his family immediately".
"The arrest and detention of 21 Savage is an absolute travesty, his U visa petition has been pending for 4 years. In...
Posted by JAY-Z on Wednesday, 6 February 2019"
He has three children who are US citizens.
"His U visa petition has been pending for four years," Jay-Z's statement continued.
The U visa he has applied for is for victims of crime, after his lawyers said he survived a shooting in 2013.
3. 21 Savage was arrested by immigration officials on Sunday
21 Savage's legal team say that he arrived in the US from the UK in 1999, aged seven.
But the USA's Immigration and Customs Enforcement (ICE) service says the musician arrived in 2005 aged 12 and went on to overstay his visa.
21 Savage's lawyers concede that the 26-year-old doesn't have the correct documents, but say they expired when he was a child, "through no fault of his own".
Jay-Z's company Roc Nation says a person charged with "visa overstay" should be allowed to be free while they fight their case.
Jay-Z is the latest star to publicly voice his support for 21 Savage.
Artists including Cardi B, Meek Mill and Offset have also called for his release.
As well as lending his vocal support to 21 Savage, Jay-Z has also hired a New York-based immigration lawyer, Alex Spiro, to assist with the case.
Mr Spiro told US showbiz website TMZ the legal team will "not stop" until 21 Savage is released.
He also denied claims from ICE that the rapper has a criminal record.
Immigration authorities said on Sunday he was charged with drug offences in 2014, but his legal team say they were subsequently removed from his record.
Mr Spiro added: "What we have here is someone who overstayed their visa with an application pending for four years - not a convicted criminal that needs to be detained and removed but, by all accounts a wonderful person, father, and entertainer who has a marijuana offence which was vacated and sealed."
21 Savage is nominated for two Grammy Awards at this weekend's ceremony, including record of the year for the chart-topping track Rockstar with fellow rapper Post Malone.