Injection molding requires two major components: pressure and heat. So your question can be broken down into those two halves: can your average extruder handle injection molding temperatures, and can it handle injection molding pressures?
Let's start with pressure.
Per this page on the University of Minnesota's site, plastic injection molding tends to require pressures of around 2 to 8 tons per square inch. Assuming you're using a 0.4 mm nozzle, which has a cross-section of 0.126 mm², that works out to be 0.000195 (1.95E-4) square inches, which translates to about 3 lb of pressure total at the nozzle assuming you're going for the high end of 8 tons (16,000 lb). However because of the way that you're treating the molten filament in the extruder as a hydraulic fluid, you've got to deal with the fact that the "piston" on one end is actually quite a lot larger area, which means you have to multiply the force by that difference in size. The cross-section of 1.75 mm filament is approx. 9.62 mm², or 0.149 in². That's 76.4 times larger, which means you need to be pushing on the end of that filament with roundabout 230 pounds, or 105 kg, of force.
For reference, the Nema 17 that's on my extruder is spec'd at 76 oz-in of torque, geared down 4:1 through a Wade's extruder, and then acting on a hobbed gear with a 6 mm effective diameter (3 mm radius). Much to my own surprise, as I write this, that means that my little plastic extruder is actually capable of just north of 160 lb of pressure force! All these numbers would need to be recalculated for 3 mm filament, and I have no experience with 3 mm, so we're going to skip that one for now.
Now, that being said, my extruder is also capable of shredding filament if conditions aren't just right. The main two problems you'll have to overcome is 1) gripping the filament hard enough without destroying it, and 2) keeping the filament from buckling. I think if you got clever with some gears keeping multiple hobbed gears synced up, and a polished aluminum or steel feed tube, you could absolutely make your own extruder that's capable of consistently putting 300+ pounds of force on your plastic filament without it buckling or stripping. The downside is that your feed rates are going to be fairly slow, so each injection molding is likely going to take you quite a bit of time. A larger motor such as a beefy NEMA23 might help offset that by giving you much higher torque at higher speeds, so long as you can melt the filament fast enough. However we'll need to revisit these pressure numbers in a few moments, after I explain a few things about temperature.
Next, let's look at temperatures. Obviously we know that we can melt the filament itself as it's moving through the extruder. Using a Volcano nozzle or something, you can even guarantee molten filament at a fairly high extrusion rate. However most printers are designed such that the filament cools to solid (60-80 °C normally) almost immediately. Injection molding designs require that the entire mass of plastic be kept molten. Fortunately, ABS and PLA melting temps are easily reached by literally any toaster oven, so stick your setup in there and you're golden, right?
But wait, there's more!
One of the problems you'll run into immediately is that extruders are carefully designed so that the plastic is molten for as little time as possible, because molten plastic against a metal tube introduces a bunch of friction, hence the need for super high pressures during injection molding. If the plastic melts too soon, then you'll clog up your heatsink (the "cold" side of the extruder), and won't be able to extrude at all. This is a fairly common source of jams in 3D printing, where you're extruding too slowly and there's not enough cooling on the heatsink. Fortunately, E3D sells a water-cooled Titan extruder that would keep the heatsink cool. However the rest of your gearing assembly, and the motor, will also need active cooling, as heat damages the permanent magnets in the rotors, and the printed geared assembly obviously will melt if put inside an oven. Your best bet might be a water-cooled Bowden setup, assuming you can find tube fittings that can withstand several hundred pounds of force. You might look into using solid tubes like brake line rather than your normal PTFE shenanigans.
Get you a water-cooled extruder, make a super-strong Bowden setup, and gear down a huge motor with a bunch of synchronized hobbed gears, and you might actually pull it off! There's plenty of Thingiverse extruder files you can use as a starting point.
As far as commercially available extruders go, however, I don't think you're going to find anything that's immediately available that can handle what you need it to without some level of modification depending on your selected injection pressures.