This church is dedicated to San Benedetto (St. Benedict) – you can see the saint's name carved at the top of the façade. In typical Venetian fashion, the name of the church was shortened to San Beneto.
San Beneto was founded in 1005 by three wealthy Venetian families. In 1229, the church was given to the monks of San Michele Brondolo (in Chioggia) by Pope Gregory IX. The church gradually fell into ruin and then in 1540, the campanile collapsed and damaged the already crumbling church. Both the church and the bell tower were rebuilt in the 17th century at the expense of patriarch of Venice, Giovanni Tiepolo (the architect is unknown).
In the de Barbari map of 1500, you can see that the old church faced in a different direction and that the bell tower had a dunce cap top similar to San Barnaba and San Polo. The new church was reoriented so that the façade faced the campo.
This is what the bell tower looks like today - it has an onion dome instead of a dunce cap.
The Patriarch of Venice website reports that “the interior is very simple and straightforward, has a single nave” but doesn’t list Mass times or opening hours. I’ve never heard of this church being open, but I don’t think it’s deconsecrated (the patriarch website lists it as a “vicariale” church under the auspices of parish church, San Luca). Is it ever open and is the art still in there? I don’t know.
Lorenzetti (Venice and Its Lagoon) praised the church’s art collection, especially the “remarkable painting” of St. Sebastian by Bernardo Strozzi (a priest from Genoa who was probably the most talented painter in Venice in the 17th century).
Lorenzetti also mentioned the two “good and imaginative” paintings of St. Benedict by Sebastiano Mazzoni (you can see one of them here).
Other works listed by Lorenzetti:
San Francesco di Paola by Giambattista Tiepolo
Virgin in Glory with St. Dominic and Archangel Michael by Carlo Maratta (on the high altar)
Virgin Mary and Saints by Antonio Fumiani (he painted that amazing ceiling in San Pantalon)
A Byzantine Madonna with silver repousse in a marble niche (sigh, I’d love to see this)
A crucifix from the workshop of Paolo Veneziano
I did stumble across this charming altarpiece, dated 1408, from the original church. It’s now in the Metropolitan Museum of Art in New York.
"Relief Altarpiece with Saints Peter, Paul, and John the Baptist. Attributed to Gerardo di Mainardo. Limestone from the Istrian peninsula, painted and gilded."
It's a signed work. Translation:
On the tenth day of October, 1408, messer Gerardo taiapera [stonecutter] made this altar to messer Saint Peter in reverence of messer Saint Lord God and of Sainted Mary and of all the Celestial Court, Amen.
San Beneto shares its campo with the 15th century Palazzo Pesaro (now the Museo Fortuny).