Prior to the square's original layout in 1863, its site was the junction of the quayside street and a historic road of Saigon that once ran through the old citadel (the ). According to scholar Vuong Hong Sen, the wharf opposite of the square was where the French naval ships anchored to
capture Saigon in 1859. Initially known as the "Rond-point", the square was planned to serve as a central point for the European city that was going to be built. By 1871, four other streets radiating from the square: rue Vannier, rue Turc, rue de Thu-Dau-Mot and rue de Yokohama (modern-day Ngô Đức Kế, Hồ Huấn Nghiệp, Thi Sách and Phan Văn Đạt, respectively) had also been opened, giving the area its present road layout. On 17 February 1879, the occasion of the 20th anniversary of the capture of Saigon, the authorities inaugurated a bronze statue of Admiral
Charles Rigault de Genouilly (1807–1873) by sculptor Alexandre-Victor Lequien (1822–1905) on the roundabout. This statue stood on a granite pedestal and was fenced off with golden-pointed railings, the Rond-point was henceforth known as
place Rigault de Genouilly. The semi-circular open space of the square, in addition to the central roundabout where the Rigault de Genouilly statue stood, consisted of three surrounding gardens with two pyramid-shaped monuments placed on two of the three gardens. The first monument in the middle garden was relocated from its original position on the riverside at the end of
rue Catinat. Mê Linh Square was also renovated with a
pond added. However, the Trưng sisters' faces and figures were said to resemble Madame Nhu herself, and a rumor started that she had asked for the statue to be modeled after her own facial features. Consequently, after the
coup d'état in November 1963, the anti-government crowd tore down the statue and rolled the broken-off head through the streets. During the
third Mongol invasion of
Đại Việt, Trần Hưng Đạo was the commander of the
naval battle on the
Bạch Đằng River which resulted in Đại Việt's victory, and thus the South Vietnamese Navy chose him as their
patron saint. The statue depicts Trần Hưng Đạo standing with his left hand holding a sword and his right hand pointing across the Saigon River. File:Saïgon - Statue de l'Amiral Rigault de Genouilly.jpg|Statue of Rigault de Genouilly and the monument of Doudart de Lagrée in the background File:Saïgon - Statue Rigault de Genouilly.jpg|Another view of the Rigault de Genouilly statue and the Lamaille monument in the background File:Me Linh Square, Saigon (48788566027).jpg|Me Linh Square viewed from above in 2019 ==Buildings surround==