Is there a minimum speed at which a vehicle can travel?

There must be a minimum amount of fuel being injected per minuscule depression of the accelerator pedal. That minimum amount of fuel will, I believe, cause a certain minimum speed once the vehicle overcomes friction and starts rolling.
Perhaps a very precise interplay of the accelerator pedal and the brake pedal by, maybe some mechanical system, might just achieve this.

yes if we dont press the accelerator the car would run on ideal air fuel mixture and if we begin to press the accelerator the throttle valve would open which leads to more rich fuel and high power which is enough to produce torque and car moves .it also depends on load of car.

It depends on the load, as well as the conditions of the wheels and the engine. What car were you driving biggie ?

The type of car isn't important in the context. I'm talking in very generic terms. Ultimately, it's the engine speed and the gear ratio that'd matter. Because I believe, with sufficient power; we can have multiple gears to reduce the speed to whatever we want (that's my theory). I think this discussion would be more meaningful provided we setup sample specifications.

Let's say the car is 1000 cc. What other specific information do we need here?

Kaustubh KatdareThe type of car isn't important in the context. I'm talking in very generic terms. Ultimately, it's the engine speed and the gear ratio that'd matter. Because I believe, with sufficient power; we can have multiple gears to reduce the speed to whatever we want (that's my theory). I think this discussion would be more meaningful provided we setup sample specifications.

Let's say the car is 1000 cc. What other specific information do we need here?

Type of gearbox? and i think CVT would suit your expectation.

Kaustubh KatdareCurious to know if there's a minimum speed at which a vehicle can travel? I'm talking about 4-wheelers and did an experiment while parking the car in the parking area. I found out that I could only bring the speed down to some level. It could be because of my driving skills; but I'm curious to know whether the engines & gearboxes are designed to operate any minimum speed? Or is it theoretically possible to have a speed of say 1 cm / hour, if we get robots to control the accelerator.

The answer is more related to sensitivity. When we press accelerator, with every degree of accelerator pressed, the fuel is ignited which results in fuel combustion (the rest is theory) and the velocity hence increases. You should have more sensitive accelerator. However, it will be detrimental to your car and most importantly life.

As @#-Link-Snipped-# said, there will be an average flow of fuel, when you start the engine.
So without pressing the accelerator your car able to move. Without pressing the accelerator pedal, Slightly release the cluth & you find it will move in a constant speed. I tried at 4km/hr.

You can look for the term "idle" for automobile engines. As KSS Manian said, even you don't press the accelerator, the motor is running. It is in idle mod. It means, the fuel pump is pumping just enough fuel to continue the cycle. In a manual car, if you slowly release the clutch while still pressing the brakes, you can see that the rpm goes down to a point and the car starts to vibrate and finally the motor "chokes". Because the forces to continue the cycle is too high to maintain by that amount of fuel.

So this is the minimum amount of fuel you can give to the motor. Now about the minimum speed, if you release the clutch completely without pressing the accelerator the car moves at a certain speed depending on the load on the car. But if you release the clutch slightly, the car can move slower because now the clutch is transferring only some of the torque to the wheels. But this can wear off the clutch so don't do this unless it is necessary.