Most of the 20 million items it contained, including the oldest human remains ever found in the Americas, are believed to have been destroyed.
The cause of the blaze is not known. No injuries have been reported.
The museum, located in a building that once served as the residence for the Portuguese royal family, celebrated its 200th anniversary this year.
The fire started on Sunday evening, after the facility had closed for the day.
Aerial images broadcast on Brazilian television showed it spreading throughout the building.
Brazil's President Michel Temer said in a tweet that it was a "sad day for all Brazilians" as "200 years of work, research and knowledge were lost".
Roberto Robadey, a spokesman for the Rio fire department, is quoted by the Associated Press news agency as saying that the hydrants closest to the museum were not working and that firefighters had to get water from a nearby lake.
By Monday morning the fire was under control and some of the museum's pieces had been rescued, he added.
t was one of the largest museums of natural history and anthropology in the Americas.
Its millions of artefacts included fossils, Brazil's largest meteorite, dinosaur bones and a 12,000-year-old skeleton of a woman known as "Luzia", the oldest ever discovered in the Americas.
The building was also home to items covering the centuries from the arrival of the Portuguese in the 1500s to the declaration of a republic in 1889.
The ethnology collection had unique pieces from the pre-Columbian era and artifacts from indigenous cultures.
Pieces from Greco-Roman times and Egypt were also on display at the museum.
The museum was established in 1818, with the aim of promoting scientific research by making its collection available to specialists.
Marcelo Moreira - a journalist with TV Globo in Rio - told the BBC: "It's very sad... This museum has a great history. It represents a lot for Brazilian history and Brazilian culture. It's really a big loss for Brazil."
In an interview with Globo, the museum's director said it was a "cultural tragedy".
Employees had reportedly previously expressed concern about funding cuts and the dilapidated state of the premises.
Brazilian President Michel Temer says the government is seeking funding from companies and banks to help rebuild the National Museum in Rio de Janeiro after it was destroyed by fire.
Education Minister Rossieli Soares said international help was also being sought and talks with the UN's cultural body, Unesco, were under way.
巴西博物馆一夜大火，2000多万文物焚毁殆尽
当地时间9月2日晚，拥有2000多万件藏品的巴西国家博物馆发生火灾，大多数藏品被烧毁。
该馆今年6月刚刚举行成立200周年庆典，是巴西历史最悠久的博物馆，也是拉丁美洲最大的自然历史博物馆之一。
一场大火吞噬了位于里约热内卢的巴西国家博物馆，这里是巴西历史最悠久的科研机构。
巴西国家博物馆有两千多万件藏品，包括美洲发现的最古老的人类遗骸。据称大多数藏品已被烧毁。
火灾发生原因尚不清楚，也没有人员受伤报告。
巴西博物馆所在的建筑曾是葡萄牙皇室的宫殿，今年还是博物馆建馆200周年。
火灾发生在周日晚间，闭馆之后。
从巴西电视台播出的航拍照片中可以看出，整座建筑都被火海吞噬。
巴西电视台当晚播放的画面显示，火光燃亮夜空，浓烟升腾，火势在有着数百个房间的博物馆建筑全面蔓延。
巴西总统米歇尔·特梅尔在推特上表示，“对所有巴西人来说，这都是一个悲伤的日子。200年的工作、研究和知识毁于一旦”。
据美联社报道，巴西消防部门发言人罗伯托·罗巴迪称，距离博物馆最近的消防栓坏掉了，消防队只能到附近湖中去抽水灭火。
截至周一早晨，火情已经得到控制，部分藏品被抢救出来。
博物馆整个三层建筑基本被烧毁，且截至目前仍存在坍塌风险。同时，国家博物馆副馆长已表示，博物馆仅有10%的馆藏得以幸存，包括陨石、矿石和部分陶艺收藏等。
巴西国家博物馆由葡萄牙国王若昂六世于1818年以“皇家博物馆”的名义创立，目前由里约联邦大学管理，馆内藏品展现了从1500年葡萄牙人发现巴西一直到巴西成立共和国的历史。
这里是美洲最大的自然历史和人类学博物馆之一。
馆内展品有动物、昆虫、土著居民的餐具、恐龙化石、埃及木乃伊、鱼类标本、哥伦布时代前的美丽陶器、南美考古器物、陨石、化石等。
巴西国家博物馆展馆内分为四个主要部分：古埃及、地中海文化、前哥伦比亚考古和巴西考古，目前馆藏2000万件。
博物馆的两千多万件藏品包括化石、巴西最大的陨石、恐龙骨骼化石，以及1.2万年前一位名为露西亚的女性骨骼化石，这也是美洲发现的最古老的人类骨骼化石。
从16世纪葡萄牙人到达巴西到1889年巴西成立共和国几百年间的藏品也珍藏在馆中。
有几件独一无二的人种学藏品来自前哥伦布时期，还有一些史前古器物来自当地土著文化。
博物馆还陈列着古希腊、古罗马和古埃及时期的藏品。
这座博物馆在1818年建成，目的是让众多专家参观展品，促进科学研究。
巴西环球电视台记者马塞洛-莫雷拉告诉英国广播公司说：“这太让人伤心了，博古馆历史悠久，对巴西历史和文化意义重大，这场火灾是巴西巨大的损失。”
巴西人类学家戈麦斯说：“巴西仅有500年历史，这座博物馆见证了其中的200年，而现在我们将永远地失去它了。”
博物馆负责人在接受巴西环球电视台采访时说，这是一场“文化灾难”。
里约市长马塞洛·克里韦拉呼吁国家重建博物馆：
国家有责任在废墟上重建博物馆，根据画作和图片重新构建每一处外部细节。即使不是原始版本，博物馆仍然能够唤起人们对赋予国家独立的（巴西）王室、（葡萄牙）王国统治时期、第一部宪法和国家团结的记忆。
据报道，之前博物馆的员工们就表达过对于经费削减和设施破旧衰败的担心。
另据央视报道，由于博物馆内多为木质结构，而且易燃物品较多，导致火灾期间火势发展迅速。
巴西文化部长塞尔吉奥·萨·莱唐3日宣布了重建博物馆的四步措施。
在第一步保护建筑和现场安全方面，巴西教育部已承诺紧急拨款1000万雷亚尔（约合1640万元人民币）。巴西教育部长罗西利·苏亚雷斯3日说：“这笔款项将立即发放，用于保证博物馆楼体不倒塌以及现场安全。”
巴西总统米歇尔·特梅尔表示，政府正寻求从企业和银行筹集资金，重建被火灾烧毁的国家博物馆。
巴西教育部长罗西利·苏亚雷斯表示，已寻求国际帮助，并开始与联合国教科文组织商讨相关事宜。
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