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yum accepts the command whatprovides (or provides) to search for installed or not installed binaries:

yum has been largely superseded by dnf on modern Fedora/RedHat-based Linux distributions; see below.

yum accepts the command whatprovides (or provides) to search for installed or not installed binaries:

dnf

dnf has a repoquery subcommand, which you can use similarly to yum whatprovides:

dnf repoquery --whatprovides /path/to/file

For example:

$ dnf repoquery --whatprovides '*/mysqldump'
mariadb-3:10.5.22-1.el9_2.alma.1.x86_64
mysql-0:8.0.36-1.el9_3.x86_64

opensuse'szypper does include the command what-provides and concerning the manual, this should also search through the contents of not installed packages. Apparently, it does not work like intended. There is a request for this feature.

zypper's search command can check file lists when used with the -f option.

zypper se -f /bin/mksh
Loading repository data...
Reading installed packages...

S | Name | Summary           | Type   
--+------+-------------------+--------
  | mksh | MirBSD Korn Shell | package

apt-file

apt-file provides the feature of searching for a package providing a binary (like Debian or Ubuntu), it is not installed by default but in the repositories.

apt-file search <path-to-file>

For example, let's search for the not installed binary mysqldump:

$ apt-file search /usr/bin/mysqldump

mysql-client-5.1: /usr/bin/mysqldump
mysql-client-5.1: /usr/bin/mysqldumpslow
mysql-cluster-client-5.1: /usr/bin/mysqldump
mysql-cluster-client-5.1: /usr/bin/mysqldumpslow

It's also possible to list the contents of a (not-installed) package:

$ apt-file list mysql-client-5.1

mysql-client-5.1: /usr/bin/innochecksum
mysql-client-5.1: /usr/bin/innotop
mysql-client-5.1: /usr/bin/myisam_ftdump
mysql-client-5.1: /usr/bin/mysql_client_test
...

yum

yum accepts the command whatprovides (or provides) to search for installed or not installed binaries:

yum whatprovides <path-to-file>

Again, the not installed mysqldump:

$ yum whatprovides /usr/bin/mysqldump

mysql-5.1.51-2.fc14.i686 : MySQL client programs and shared libraries
Repo        : fedora
Matched from: 
Filename    : /usr/bin/mysqldump

mysql-5.1.51-1.fc14.i686 : MySQL client programs and shared libraries
Repo        : fedora
Matched from: 
Filename    : /usr/bin/mysqldump

zypper

opensuse'szypper does include the command what-provides and concerning the manual, this should also search through the contents of not installed packages. Apparently, it does not work like intended. There is a request for this feature.

Webpin provides a webbased solution, there is even a script for the command-line.

pkgfile

Available as pkgtools for pacman based systems. Provides a similar search feature like the others above:

$ pkgfile -si /usr/bin/mysqldump

Name      : mysql-clients
Version   : 5.1.54-1
Url       : http://www.mysql.com/
License   : GPL
Depends   : libmysqlclient
...

apt-file

apt-file provides the feature of searching for a package providing a binary (like Debian or Ubuntu), it is not installed by default but in the repositories.

apt-file search <path-to-file>

You may want to update once before searching...

apt-file update 

For example, let's search for the not installed binary mysqldump:

$ apt-file search /usr/bin/mysqldump

mysql-client-5.1: /usr/bin/mysqldump
mysql-client-5.1: /usr/bin/mysqldumpslow
mysql-cluster-client-5.1: /usr/bin/mysqldump
mysql-cluster-client-5.1: /usr/bin/mysqldumpslow

It's also possible to list the contents of a (not-installed) package:

$ apt-file list mysql-client-5.1

mysql-client-5.1: /usr/bin/innochecksum
mysql-client-5.1: /usr/bin/innotop
mysql-client-5.1: /usr/bin/myisam_ftdump
mysql-client-5.1: /usr/bin/mysql_client_test
...

yum

yum accepts the command whatprovides (or provides) to search for installed or not installed binaries:

yum whatprovides <path-to-file>

Again, the not installed mysqldump:

$ yum whatprovides /usr/bin/mysqldump

mysql-5.1.51-2.fc14.i686 : MySQL client programs and shared libraries
Repo        : fedora
Matched from: 
Filename    : /usr/bin/mysqldump

mysql-5.1.51-1.fc14.i686 : MySQL client programs and shared libraries
Repo        : fedora
Matched from: 
Filename    : /usr/bin/mysqldump

zypper

opensuse'szypper does include the command what-provides and concerning the manual, this should also search through the contents of not installed packages. Apparently, it does not work like intended. There is a request for this feature.

Webpin provides a webbased solution, there is even a script for the command-line.

pkgfile

Available as pkgtools for pacman based systems. Provides a similar search feature like the others above:

$ pkgfile -si /usr/bin/mysqldump

Name      : mysql-clients
Version   : 5.1.54-1
Url       : http://www.mysql.com/
License   : GPL
Depends   : libmysqlclient
...