“We are looking into the origin of the funds he used to buy her expensive gifts and luxurious properties,” Judge Ghada Aoun said.
In March, Mr Salameh and his brother, Raja Salameh, were charged with illicit enrichment.
Saliba is known to be a close acquaintance of the central bank chief. She has starred in popular TV series Above the Clouds and Moment of Silence and has 2.3 million Instagram followers.
Ms Aoun issued the order to bring the actress in for questioning last week, Reuters reported, but security forces had yet to enact it.
Once praised as the man who kept Lebanon’s banking sector thriving, Mr Salameh is now facing investigations into his personal wealthin at least five European countries.
As part of these probes, the EU's Hague-based criminal justice agency last March froze €120 million ($124.3 million) worth of assets belonging to him and his entourage.
Last week, the investigative journal Mediapart reported that French prosecutors had indicted a former partner of Mr Salameh for criminal conspiracy, organised money laundering and aggravated tax fraud laundering.
Anna Kosakova, a Ukrainian woman who lives in France and has a daughter with the central bank governor, is the first person to be prosecuted in the case.
A spokesman for Lebanon's Central Bank did not reply to a request for comment, but Mr Salameh has repeatedly denied allegations of corruption.
He said that his wealth, which he estimates at $23 million, has been lawfully acquired and that it comes from his investments made as a banker before becoming central bank governor in 1993.