The train, on a route frequently used by foreign delegations returning from Kyiv, was attacked just 2km from the Polish border, Ukraine's railway operator said.
The visitors were on their way back from a security conference in Kyiv.
"It is highly probable that the Russian drone's intended target was in fact the diplomatic train, which had departed the station earlier than scheduled," the company said in a Telegram post.
Bildt shared a video on X of the attack at Yahodyn station, near the Yahodyn-Dorohusk border crossing with Poland.
"This wasn't our train, but the one just minutes after us by the Polish border crossing," the former Swedish prime minister said.
"It was evacuated as the Russian drone approached and no one was hurt. Very good safety system. Our train just had an evacuation warning."
Bildt, Johnson and fellow passengers had been in Kyiv for the Yalta European Strategy conference, which is an annual gathering of leaders and experts across politics, business, security and media.
Another train, with former CIA director David Petraeus on board, was still at Yahodyn station when the drone struck, according to Ukrzaliznytsia.
There were no reports of casualties on any of the trains.
Ukrzaliznytsia said it "constantly adjusts train schedules" to guard against strikes.
"I don't know what warped logic drove (Russian President Vladimir) Putin to blow up a stationary Ukrainian locomotive on the Polish border this morning," Johnson wrote in a post on X.
"What we can say for sure is that this is the kind of random and senseless attack Ukrainians are enduring every day - even on civilian railways," he added.
Earlier on Sunday, a Russian drone hit a truck less than a kilometre from Polish territory, according to border guards, forcing the temporary closure of the Yahodyn-Dorohusk crossing.
Russia's defence ministry said it had targeted infrastructure facilitating military cargoes from Europe in western Ukraine.
with Reuters
