The garda investigation into his death has now been upgraded to a murder inquiry.
A post-mortem exam is expected to be carried out on his body today to determine the exact cause of death.
Mr Rzeszutko was surrounded by his partner and family when the decision was made to turn off his life-support machine.
Mr Rzeszutko, from Olsztyn in Poland, had been living with his partner in Clarehall, north Dublin, since 2007.
Three males were arrested over the weekend in relation to the attack.
Edward Byrne (20), with an address at a Dublin 8 YMCA hostel, was charged with assault causing harm yesterday at Dublin District Court.
Defence solicitor John Feeney told Judge McHugh that his client, who remained silent during the proceedings, was deferring a bail application until Friday next.
Judge McHughremanded the accused in custody to appear at Cloverhill District Court on Friday.
The two other males arrested, who are both teenagers, were released without charge and a file is being prepared for the DPP.
Mr Rzeszutko was discovered by security staff at the industrial estate at around 5am on Saturday in an unconscious state and was immediately brought to Beaumont Hospital.
Gardai said last night they had interviewed a large number of people in connection with their inquiries.
One investigator said: "Mr Rzeszutko was an innocent man, who had come here from Poland to find work. He was minding his own business while walking to his job when he was suddenly attacked."
Shocked colleagues at the Kish Fish processing plant were too upset to speak about the tragic death but in a statement the company described him as an "exceptional colleague".
"Our thoughts and prayers are with Lukasz and his family, here in Ireland and in Poland," the statement added.