Heinrich Albert was born in Würzburg and initially learned violin and horn, studying the latter at the Königliche Musikschule [Royal Music School] Würzburg (1881–8). Following his studies he played in various orchestras in Germany, Sweden, Switzerland, and Russia. Between 1895 and 1900 he was a member of the Kaim Orchestra, the predecessor of the Munich Philharmonic, playing under such renowned conductors as Felix Weingartner, Arthur Nikisch, Ferdinand Löwe, and Gustav Mahler. Around 1892 he began to teach himself the guitar, aided, from about 1905, by Luigi Mozzani. His performing career, both as guitarist and as conductor of a mandolin orchestra, lasted from 1900 to 1943. In 1900 he began to establish himself as a full-time teacher of guitar and mandolin in Munich. Among his most prominent pupils were Luise Walker and the comedian Karl Valentin. In 1909, he was appointed "Kammervirtuose" [chamber virtuoso] by Marie of Bavaria. Around 1910, he founded a unique guitar quartet following the principles of the string quartet, using instruments in various sizes. Apart from his compositions and arrangements, Albert edited a number of guitar tutorials, notably the Moderner Lehrgang des künstlerischen Gitarrespiels (5 volumes, 1914–9). The increasing success of the Spanish approach to the guitar after 1920 seems to have frustrated him.
The Hamburg-based Heinrich Albert Duo is named after him. In 2007, they issued a CD with the collected duos by Albert (see 'Selected recordings').
Albert's 5-volume guitar method was unrivalled in German-speaking countries for several decades and have unjustly fallen into neglect, as several experts acknowledge their value to this day.
As a composer, Albert was a Classicist, occasionally using a freer harmonic approach with an accessible degree of technical difficulty. Some of his music makes use of elements of Italian and Spanish folkmusic. His works were played by most major guitarists in the first half of the 20th century. He was then largely forgotten and has been rediscovered only after around 2000.