Newt was on trial for his part in violation of the International Statute of Secrecy.
It’s likely that Newt’s travel ban was because of his participation in events that violated the Statute of Secrecy.
“TRAVERS
Hearing commences.
The quill begins to write. TRAVERS opens a file in front of him, which contains pictures of NEWT’S Wanted pictures and of the post-Obscurial devastation in New York.”
- Fantastic Beasts: The Crimes of Grindelwald
In the foreword to the new edition of Fantastic Beasts and Where to Find Them, Newt mentioned his inadvertent involvement in breaching the Statute.
“At President Picquery’s request, I made no mention of the more important American magical creatures in the first edition of Fantastic Beasts, because she wished to deter wizarding sightseers. As the American wizarding community was subject to greater persecution at that time than their European counterparts, and given that I had inadvertently contributed to a serious breach of the International Statute of Secrecy in New York, I agreed.”
- Fantastic Beasts and Where to Find Them (updated edition)
This is likely to be why the Ministry could justify banning Newt from international travel.
However, it was likely at least partially an attempt to blackmail Newt into cooperation, since the Ministry was suspicious of him and Dumbledore.
Though Newt was involved in the events in New York, it seems highly likely that the Ministry’s reason for banning Newt from international travel, and for interrogating him on his part in events in New York was because they suspected Newt was working with Dumbledore.
“GUZMAN
Mr. Scamander, it’s clear you’re frustrated and, frankly, so are we. In the spirit of compromise, we’d like to make a proposition.
NEWT glances at THESEUS warily. THESEUS nods: Listen.
NEWT
What kind of proposition?
TRAVERS
The committee will agree to lift your travel ban under one condition.
NEWT waits. SPIELMAN leans forward.
SPIELMAN
You join the Ministry. Specifically, your brother’s department.”
- Fantastic Beasts: The Crimes of Grindelwald
The Ministry suspects that Newt is following Dumbledore’s orders, and they do not trust Dumbledore.
“TRAVERS
Newt Scamander is in Paris.
DUMBLEDORE
Really?
TRAVERS
Cut the pretense. I know he’s there on your orders.”
- Fantastic Beasts: The Crimes of Grindelwald
The Ministry suspected that Dumbledore may have been attempting to sabotage them in their attempts to stop Grindelwald.
“TRAVERS
There’s a rumor this prediction refers to the Obscurial. They say that Grindelwald wants—
DUMBLEDORE
—a highborn henchman. I’ve heard the rumor.
TRAVERS
And yet Scamander appears wherever the Obscurial goes, to protect him. Meanwhile you have built up quite a little network of international contacts—
DUMBLEDORE
(quiet, steely)
However long you keep me and my friends under surveillance, you’re not going to discover plots against you, Travers, because we want the same thing: the defeat of Grindelwald. But I warn you, your policies of suppression and violence are pushing supporters into his arms—”
- Fantastic Beasts: The Crimes of Grindelwald
Dumbledore is also trying to stop Grindelwald, just with less collateral damage than the Ministry’s methods, but the Ministry doesn’t know that. Due to his history with Grindelwald, they believe he may be on Grindelwald’s side. Banning Newt from international travel would have given them the chance to use the promise of its lifting to attempt to get information out of Newt, then to blackmail him into helping them kill Credence, and if he still refused to join them, hindered him from going on missions for Dumbledore.