"Indifference": the word, carved in huge letters in a grey concrete wall, welcomes visitors to the site behind the north Italian city's central station, also known as "binario 21" (platform 21).
The memorial opened in 2013, under the platforms, at the exact spot where hundreds of Jews were locked into livestock railcars, hoisted up to the tracks by a mail-carriage lift, and sent on their way to concentration camps.
For the past week the cold, solemn site, which lies mostly underground, has found a second calling as a haven for around 35 mainly Eritrean and Ethiopian migrants.
"We say one must fight indifference. We cannot remain indifferent ourselves" to the plight of hundreds of migrants who mass each night at the station, Roberto Jarach, deputy head of the Memorial Foundation, told AFP.
Around 70,000 people have been picked up so far this year during attempts to cross the Mediterranean to Italy, and a crackdown on security at European borders has seen the numbers of migrants sleeping rough in Milan swell.
Inside the memorial they bunk down side by side, their beds hidden from the public gaze behind partitions, just metres from the exhibition of railcars, photographs and video installations with the names of the deportees.
At the crack of dawn, many have already left to catch trains north in a bid to cross the border. Others nibble on biscuits distributed by volunteers from the Catholic Sant'Egidio community, as trains rumble past overhead.
Gemal, a 26-year old Eritrean who fled his country in 2003 and passed through Sudan and Israel before ending up here, says in basic English that he "slept very well" and appreciated the food and shelter.
He hopes to join his brother in Germany "as soon as possible". Fellow Eritrean Luwame, 20, is heading for the north too, red Crocs on her feet, in the hope of making it to Sweden.
Stuffed animals and toys are placed on beds for migrants inside the Shoah Museum - Binario 21 ('Platform 21'). Photo: Giuseppe Cacace/AFP
Using the museum to shelter migrants was suggested two months ago when an influx of Syrian refugees forced the city's mayor to look outside the box for housing solutions.
At the time the museum was considered impractical, but the idea stuck and the cloakroom was transformed into living quarters in just a day and a half.
The migrants have access to the venue's high-design washrooms, where a shower has just been installed.
"The taps are electronic, not the easiest things to shower with," jokes Jarach.
How long will the migrants sleep there? Sant'Egidio will assess the situation monthly, but he believes the numbers will remain high unless the security situation at Italy's borders eases.
Liliana Segre, 85, was deported in 1944 from "binario 21" when she was 13 years old, along with her father, who perished.
"Seeing armed men push people back reminded me of things I will never forget even if I live to be 100 years old," she said, referring to recent clashes between migrants and French border police in the Italian town of Ventimiglia.
She compared people traffickers who send migrants to sea in rickety boats to those Italians who betrayed Jews desperately trying to get to Switzerland, by turning them over to the authorities after robbing them.
The word "indifference" at the entrance to the museum is an important reminder, she says, of the risks faced when people close their eyes to evil.
"Indifference towards people like me, guilty only of being born Jewish, pained me so much before, during and after the persecution, it still does now."
"I know the word shocks... but if we are not shocked, there is no hope left," she said, adding that she'd like another word to be displayed: "you".
"You, turn around. Look at other people."