For months, pro-Russian separatists have fought Ukrainian forces in two eastern regions of Ukraine but a fragile ceasefire has been agreed by both sides.
Despite repeated violations of this truce, Babatunde signed a one-year deal with Ukrainian Premier League side Dnipro last week after terminating his contract at rivals FC Volyn Lutsk.
I have been playing in this country for four years and I feel very safe to continue my professional career here
"The club and league organisers have taken every precaution with the security of the players, officials, fans and everyone involved in Ukrainian football," he told BBC Sport.
"Life here is normal and they've also ensured that we don't travel or play where there are security concerns.
"I have been playing in this country for four years and I feel very safe to continue my professional career here."
The 22-year-old made his debut for 2015 Europa League finalists Dnipro when they beat Shakhtar Donetsk 2-0 at the Chornomorets Stadium in the Black Sea city of Odessa on Friday.
The nine-time Ukrainian champions Shakhtar are homeless because their Donbass Arena was shelled during fierce battle last year.
Amid all this turmoil in the Eastern European country, Babatunde insists he felt safe in Odessa, the scene of a major fire last year.
"I know Shakhtar couldn't play in Donetsk, but the game took place in Odessa and not Lviv, but it was a good game and atmosphere," he said.
"I am a footballer so my focus was on the football and we felt safe and happy to beat Shakhtar away."
The skilful winger, who has been in Ukraine since 2011, rejected offers from Norwegian and Chinese clubs to play European competition with Dnipro.
"I'm very familiar with the country and league but Dnipro also provides the opportunity to play in the Europa League.
"The club reached the final of the competition last season and they are hungry to go a step further this season.
"We have a good team and I have a strong feeling that we can achieve something as a team," Babatunde added.
Babatunde, who made his international debut against Mexico in June 2013, played for Nigeria against Chad in a recent 2017 Africa Cup of Nations qualifier in Kaduna.
He also represented his country at the 2013 Fifa Confederations Cup and the 2014 Fifa World Cup.
One of Nigeria's standout performers at the World Cup in Brazil, he suffered a fractured wrist in the final group game against Argentina.
He underwent surgery and missed the rest of the World Cup before a lengthy spell on the sidelines kept him out of international football.
But a fit-again Babatunde made an emotional return for the Super Eagles 2-0 win against Chad in June.
Nigeria international winger Michael Babatunde says he feels "very safe" playing in Ukraine despite the current political instability in the country.