Hasina, re-elected in December in polls marred by violence, mass arrests and claims of rigging, has been accused of increasing authoritarianism.
Mohammad Monir, 35, was found guilty late on Wednesday by a Dhaka cyber tribunal for doctoring and publishing on social media images of Hasina and ex-president Zillur Rahman.
“He posted those distorted images in his Facebook status and made derogatory remarks in the photo captions,” prosecutor Nazrul Islam Shamim told AFP news agency.
He was convicted under section 57 of the South Asian country’s Information and Communication Technology (ICT) law.
Shamim said that since the cyber court began functioning in 2013, at least seven people have been sentenced to jail for similar offences involving Hasina and others.
At least 200 more such cases are pending and in various stages of the trial, he said.
Rights groups have documented how the ICT laws have been used to silence criticism in the country of 165 million people.
The most high-profile arrest made under the law was that of acclaimed photographer Shahidul Alam in July last year, hours after he spoke to Al Jazeera on the student protests in the country.
Released on bail in November after more than 100 days of incarceration, Alam still faces a maximum of 14 years in jail if convicted.
In recent months, the ICT laws have been replaced by Digital Security Act, which critics say gives the authorities even wider powers to curb freedom of expression – a charge rejected by the government.
In its election manifesto, the opposition Bangladesh Nationalist Party (BNP) had vowed to scrap the digital law.