The destruction was the result of violent protests that have swept the country in recent weeks calling for the scrapping of quotas on government jobs.
Security forces are accused of excessive force against student protesters, with at least 150 people killed in protests so far.
Many said Ms Hasina had not appeared to express the same level of sympathy towards those who had died, or their families.
The pictures were taken during Ms Hasina's visit to a metro rail station in the city of Mirpur on Thursday, where ticket vending machines and the signalling control station were shattered. Ms Hasina was pictured frowning and wiping her tears with tissue paper.
"What kind of mentality leads them to destroy facilities that make people's lives easier? Dhaka city was clogged with traffic. The metro rail offered respite. I cannot accept the destruction of this transport facility made with modern technology," Bangladeshi daily The Business Standard quoted the prime minister as saying.
These comments drew the ire of Bangladeshi internet users.
"We lost [hundreds of] students. But PM Sheikh Hasina had the time to go "cry" for a metro rail, not for the people who won't return ever again," said one Twitter user.
"Shedding crocodile tears for a railway track while others [have died]...." another chimed in.
Journalist Zulkarnian Saer, who has in the past spoken out against the government, said: "Hasina had the time to visit the vandalised train station, but she did not visit [the families] of the students... shot dead [during protests]."
Some called the photographs an attempt to drive attention away from deaths from the protests.
"No doubt that she went there to ... get some attention and empathy," said one Facebook user.
Security forces have been accused of using excessive force to quell the unrest, but Ms Hasina had instead blamed her political opponents for the wave of violence.
Her government is working to "suppress these militants and create a better environment", the 76-year-old said earlier this week, adding she was "forced" to impose a curfew for public safety.
Kelly Ng