The rapper and songwriter said she would never condone Nazism in her art.
She added that both the producer and the person in charge of the video "happen to be Jewish".
The video also features rapper Drake, who is half Jewish.
Minaj said the video had not been influenced by Adolf Hitler's party but by a cartoon called Metalocalypse and also by Sin City, the comic book that was made into a film.
The director Jeff Osborne has been retweeting both positive and negative reviews of the video.
Her apology came after Anti-Defamation League, one of the top civil rights agency in the US said the video used "Third Reich imagery".
They argued the video was "a trivialization of the history of that era".
In the video Nicki Minaj is portrayed wearing a black body suit with stylised black letters on her chest. Some fans said this resembled a swastika.
Long red banners bearing the logo hang above her as she sits at the end of a corridor of tanks.
Guns fade across the screen as a drawing of Chris Brown in an authoritarian uniform flashes up, the logo emblazoned on his cap.
Troops in futuristic outfits are also drawn into the video, as well as grim reapers, futuristic flashing gas masks and storm trooper-type characters who appear to fan Minaj.  The ADL welcomed her apology, adding "We hope that she will take further steps to educate herself and her fans about who the Nazis were and why we should never take genocide or the Holocaust lightly."
Her full Twitter comments can be seen below.

Sales volumes were 1.3% higher in the month compared with March.
They were also 4.3% higher than a year earlier, the Office For National Statistics (ONS) said.
The ONS revised March's retail sales figures, showing retail sales fell by just 0.5% rather than 1.3%, as first estimated.
"Clothing stores remain the main drag on growth in the retail sector, with sales hampered by unseasonal weather. However... sales increased in April compared with March as lower prices boosted sales," said ONS statistician Melanie Richard.
Colder than usual weather had also dented spending in March, hurting demand for spring and summer clothes, according to the ONS and surveys from the British Retail Consortium and the CBI.
The latest ONS figures showed total average store prices in April were 2.8% lower than a year earlier, dragged down by a 7.3% drop in fuel prices. Food store prices fell 2.3% amid the continuing supermarket price war.
However, the total amount spent in April increased by 2.1% to Â£28.1bn compared with the year before.
Keith Richardson, of Lloyds Bank commercial banking, said a rush to complete property deals before a stamp duty rise came into effect in April had helped to boost demand for household goods and furniture.
Vicky Redwood, chief economist at Capital Economics, said that consumer confidence did not seem to have been adversely affected by the UK's upcoming referendum on EU membership.
"Indeed, consumer spending should prevent the economy from slowing too much this quarter, even if referendum uncertainty has a bigger impact on business confidence and investment," she said.
The British Chambers of Commerce (BCC) said the rise in April's retail sales was welcome, but highlighted imbalances in the UK economy.
"After the disappointing decline in March, the strong retail sales recovery in April supports our view that in spite of major headwinds the UK economy continues to grow, albeit at a slowing pace," said David Kern, BCC chief economist.
"However, the contrast between buoyant retail sales and the problems facing other sectors such as manufacturing highlights the unbalanced nature of Britain's recovery."
The BCC called for "a more balanced economic structure with a stronger focus on exports, investment and manufacturing".
The stronger-than-expected retail sales figures pushed up the value of the pound. Sterling rose against the euro by 0.3% to â‚¬1.3053, and climbed 0.2% against the dollar to $1.4625.
Nicki Minaj has apologised after the lyric video for her 'Only' track was accused of containing Nazi imagery.
[NEXT_CONCEPT]
UK retail sales volumes rose strongly in April despite lower spring clothing sales due to the cold weather, official figures show.