(Assuming you already have akmod-VirtualBox and kernel-devel installed.)
This is not limited to Fedora 24 and it happens a lot after kernel updates. With every newly installed kernel, the VirtualBox kernel modules need to be rebuilt. This is done by the akmods tool and for the build to succeed, the kernel headers (kernel-devel) need to be installed.
In theory, it should just work automatically. When you reboot after installing a new kernel, the system should automatically call akmods, which would then build the kernel modules for VirtualBox. Unfortunately, the reality is that it does not always work. In some rare cases, it may be that the build fails because something in the kernel has changed (example: bug 14227 version 4.3.28). In this case, you might select the previous kernel in the boot menu until an updated version of VirtualBox has been released.
However, if this error (Kernel driver not installed (rc=-1908)) is shown, it's likely that the build failed or did not run for another reason, so the first thing to try is to run the build manually and see if that works.
Open a terminal, become root and run this command to build the VirtualBox kernel modules:
# akmods --force
If should say "OK":
Checking kmods exist for 4.9.13-201.fc25.x86_64 [ OK ]
Building and installing VirtualBox-kmod [ OK ]
If it did not say "OK", you may be missing some header files (dnf install kernel-devel and reboot) or the build might indeed fail because something in the kernel has changed and VirtualBox needs to be updated accordingly.
Note that kernel-devel (without -$(uname -r)) installs the latest version from the repository, so after updating the kernel, a reboot is usually required. Also note that akmods may have to be run with the --force option as shown above, especially when running the build manually. If you forget this option, it might simply show a warning and not do anything (Bug 4485):
Ignoring VirtualBox-kmod as it failed earlier [WARNING]
If it did say "OK", load the modules (or reboot):
# systemctl restart systemd-modules-load
If the above steps failed, check the log file (/var/cache/akmods/akmods.log), the VirtualBox version (rpm -qi VirtualBox), your Fedora release (cat /etc/fedora-release) and kernel version (uname -r). If the build fails because of an incompatibility, you might consider opening a bug report using this information.
If you installing VirtualBox on a UEFI machine you need to sign your kernel modules or disable UEFI, You should follow rpmfusion.org Virtual box kernel module installation, is is the best way to maintaint virtualBox in Fedora. Personally will recommend to use KVM with virt-manager or boxes and avoid using VirtualBox and all its issues.
Wrong,... You can't disable UEFI. You got UEFI or BIOS. What you can dis-/enable is Compatibility-Mode (Legacy-Mode) and a UEFI-Feature called SecureBoot. This vboxdrv-issue is about SecureBoot. Take a look at this for further information.
Right I mean disable secure mode on UEFI.