The FBI "took several steps in a variety of areas to identify and reduce security vulnerabilities" after the incident, the agency told BBC News.
Daniela Greene lied to her employers about her 2014 trip, reports CNN, which broke the story.
The 38-year-old served two years in prison after fleeing back to the US.
Greene's story was ordered to be kept secret by a US judge, but was revealed for the first time on Monday after federal court records were unsealed.
US officials claimed to have killed Cuspert before, but later retracted that statement
The man whom Greene married, Denis Cuspert, is a German rapper-turned-IS recruiter.
In February 2015, the US government labelled him a specially designated global terrorist.
In one propaganda video he was seen holding a freshly decapitated human head.
Greene, who worked at the FBI's Detroit field office, was tasked in January 2014 with investigating Cuspert, according to CNN.
Six months later the German-speaking linguist travelled to Syria to marry him.
Czechoslovakia-born Greene told her work superiors she was planning a trip to visit her parents in Germany.
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But instead she travelled to Turkey where she crossed the Syrian border with the help of local IS operatives, reports CNN.
Greene was still married to a US serviceman at the time.
Shortly after arriving in Syria in June 2014, she reportedly married Cuspert.
He had dropped his stage name of Deso Dogg to call himself Abu Talha al-Almani.
But Greene apparently soon had second thoughts about her new husband.
According to CNN, she wrote to one unidentified person in the US: "I really made a mess of things this time."
The next day she added: "I am gone and I can't come back.
"I am in a very harsh environment and I don't know how long I will last here, but it doesn't matter, it's all a little too late."
Within one month of arriving in Syria she had fled the country and returned to the US.
What is life like for women under IS?
"Nour" is a woman from Raqqa, the so-called Islamic State's (IS) capital inside Syria. She managed to escape the city and is now a refugee in Europe, where she met up with the BBC.
This story is based on her experiences and those of her two sisters, who are still inside the IS-held city.
She admitted to investigators that she had told Cuspert he was the target of an FBI investigation, reports CNN.
It is unclear how she managed to flee the IS-held territory.
Greene pleaded guilty in December 2014 to making false statements involving international terrorism.
She served two years in a federal prison and was released last summer.
Greene currently works as a hostess at a hotel at an undisclosed location.
According to court documents obtained by CNN, prosecutors labelled her actions "egregious" and deserving of "severe punishment".
But Greene's relatively lenient sentence was because of her "significant, long-running and substantial" co-operation with authorities, prosecutors said.
Her lawyer, Shawn Moore, told CNN that Greene was "smart, articulate and obviously naive", adding that she was "genuinely remorseful".
"She was just a well-meaning person that got up in something way over her head," Mr Moore added.